mounting and bolting

You've got two problems. 
First, congrats on the flying dismount!  BTDT! Did you forget to let go of the reins and try to hold on to her?  BTDT, too!  Except I got drug before my brain told my hand to release.  UGH!
Sometimes, once you trust your horse, it's not as scarey for them to take off because, unless they are in top condition, they ain't gonna run forever!  So maybe try sticking with her and the other horses will stop or you can circle her and make her work.  I know people are going to tell you to teach her the one rein stop.  When a horse is flat out running, I really don't feel comfortable pulling their head to one side.  I'm picturing somersaults here.  AND yes, your horse should do everything you want every time you ask it....  SO I'll leave this problem alone because it IS a safety issue and I think it has to do with "who's the boss" which has something to do with your next problem, which I'll address! []
You have to have LOTS of time on your hands.  OR, if you've only got limited time with your horse, plan on spending the whole time on this lesson.  She has to stand for you because, like last weekend, someone on the trail ride might have to get off and then what?  I ended up getting off and giving the girl a leg up - it was a disaster - she had a bad knee, the horse wouldn't stand...  I wanted to jerk a knot in that horse but... not my place. 
SO get yourself a GOOD mounting block and a dumptruck load of patience.  Put your anger in the trunk of your car and DON'T bring it out under any circumstance. []  Your horse needs to feel secure around you for her to accept you as leader.  Smacking on her won't speed up the process in the least!  SO, you groom and tack up as usual....  Put her at the mounting block and tell her to stand, using whatever word you choose for that.  Go to get on, (don't plan on it, you know what comes next) she starts to walk off.  At the first sign of her stepping you stop her with the rein and jump down, back her up right where you first put her.  Does she back up good?  If not, that's another lesson you need to have under your belt.  Ground work, ground work, ground work.  So you have her back at the block, do it again all over.  Like John Lyons says "after about 200 times, she will get the idea".  Patience, patience, patience.  Don't let anyone come along and say "do you want me to hold her for you?"  NO, she needs to learn.  And don't tie her to mount!  Never!  BE PATIENT!  I'm sure she's a wonderful horse or you would have never fallen for her.  You both need to learn each other's signals. 
My Zag needs standing lessons, too.  I need to fix my standing tree and let him stand!  He'll get the hang!  It took a long time for me to trust Zag and there are times he makes me wonder but I stay calm and let him do a few things to get his mind to focus, serpenines, circles, backing up..... yielding to leg pressure.
I hope it all goes well and POST SOME PICTURES!!  We need pictures!!  []

Hunter is right.  It takes patience and time, plus some finesse   I just finished teaching my young horse to do this.  I use a mounting block so it's easy to get on and off.  When you go to mount, make sure you aren't poking her with a toe.  Have the rein closest to you shorter so if she moves, she will have to turn toward you and can't really go forward.  Put weight in the stirrup.  If she moves, take your weight off the stirrup, pull that inside rein to stop her, back her up to where she should have been and tell her "whoa, stand or whatever your command is"  Once you've successfully got her holding still with just weight in the stirrup, praise her profusely.  Just continue to add steps from weight in stirrup to swinging leg, to sitting lightly in the saddle.  Some people plop down in the saddle which would make anyone shoot forward so be sure to let your weight down in a controlled manner.  We had a mare that wouldn't stand and she did great if she got a carrot once you were on!
 
The bolting issue can be scary.  Now that you know she is likely to bolt, try to request that your riding buddies warn you before they take off so you can get yourself together.  I usually don't bail unless there's a low-hanging branch up ahead.  As Hunter said, most horses won't run for long or your "friends" will see you're in trouble and stop.

thank you for the replys. i will try what you have said to do. i just dont understand when i went to see her before i bought her she did everything i asked her to do with no problems but having her here is just uuhhhh..... when i finally get mounted and try to get her out of the drive to go riding up the road she won't go unless another horse goes first and turning her is a fight to go where i want her to. they said she was used for trail riding alot.. would that make a difference on where she goes? we have private road out in the sticks so there is not much traffic. she does okay when they drive by or she will stand in the middle of the dirt road and refuse to move!!!!

I just said today my horse does SO much better when I trailer him to ride than when we ride around the neighborhood!  Are you a fairly good rider?  Do you feel secure using a crop on her?  Just having one in your hand and giving a tap behind the saddle might get her attention.  (I'm not saying hit her but she's testing you.)  Stay relaxed.  Figure out ways to work her when she isn't listening like circling her or getting her to flex her nose to your boot.  If she wants to go back you make sure you work the stew out of her when she gets back.  Then try to leave again?  Maybe?  I wish trainer101 or HG would show up.  They're the real trainers!  I know she's going to turn out great! 
When you tried her out, her alpha was the person you bought her from maybe.  She's not seeing you as alpha, I don't think.  Not yet, but she will.  Have patience and don't give up. 

Hi welcome to the forum.  Forgive my sloppy typing its been awhile since I have been on the computer!  First I have some questions for you.  How long have you had her?  How many times has she tried to take off on you?  How often do you ride a month?
 
The reason I ask and I can tell you better with some more info from you but if you have had her for a while now and she has just started this I would recomend getting her vet checked.  Could be somehting is pinching or pulling her with the saddle as you are mounting and she is just tired of it.  Do her ears stay forward or do they lay back at you when you step up?  Does she start with her head low and relaxed then raise it as you begin to get on?  It could be that you have been pulling the saddle to you without even realizing it causing the saddle to pinch her withers instead of using your legs to push you up.
 
First lets work on the taking off thing.  What kind of bit are you using?  Is is a snaffle or a shank bit (any bit with shanks is not a snaffle even if the mouth piece is broken)?  If it is a shank I would take her back to a snaffle bit for a while till you get her thinking again.  First thing is to move her around a bit saddled up and everything.  Get her feet moving, don't worry about trying to get on just put that to the back of your mind.  Think about what she is doing right now.  Is she swishing her tail, is she moving out relaxed and settling nicly or is she nervous and trying to pull you back to the pasture?  These are all things you should be aware of BEFORE moving on.  Depending on her age she more than likely knows she is doing something wrong but just in case its easier to go back to the begining especially if you just got her and are wanting her to look to you for leadership.
 
Once you have all this info stop her and take a moment to pet her and rub all over her face.  Now is the time to teach her how to yeild ot the bit again.  Teach her how to flex her head around both ways until she is light and  not spinning circles.  I have an article on here (January edition) that goes over how to start teaching your horse to flex.  Then flex her head and slap the saddle, stirrups, her belly and really give her a good check.  If anything startles her go back and work on it till she stops spinning and relaxes.  (Another article on here goes over that)  When she is relaxed and calm with all that then move on to flexing her head and pretending to get on.  Jump up and down, move your leg as though you were puting it in the stirrup.  Each time she tries to take off you have her head tipped to you so all she can do is circle.  Stay with her till she stops and then pet her.  When she is ok with that then flex her head and step up but don't sit down, lean over the saddle and rub where your other foot will go, rub her shoulder, but keep her head flexed around to the toe of your boot.  If something here bothers her then you can go back and fix it before you ever endanger yourself further. 
 
I have done this with colts just learning and older horses that want to bite, bolt and spin, it works and it shows you where the holes in your horses foundation really are.  It shows you what you need to work on with your horse to have a better relationship  and what YOU yourself need to work on to be the leader to give her confidence.
 
Sometimes I do this for several days before actually putting my hinny in the saddle and even then I usually don't ask them to move out but just sit there and flex them from side to side then get off.  Then get back on again, then off and right back on.  Some horses realize really quickly that they are not going anywhere and calm right down while others still get paniced and want to move off so use your judgment on how far you want to go each day.
 
I will bump those articles up for you.  I think there could be something there you could use.  If you have problems or need some help just give me a holler.  You can e-mail me or give me a call, I think my info is still in here somewhere.  LOL  The most important thing is to have fun and stay safe. 

i will try all the advise that has been given. its kinda muddy out and everyone says not to ride but if i wait for this to dry up i'll be waiting till spring!!. ive had her for a few months now. she is a tenn walking horse about 4-5 yrs old. i was told that she has been trail rode her whole life so far. is there a difference in trail ride then just riding around? when i get ready to mount i put my foot in sturip and she starts to move away. i haven't noticed her ears laid back or anything i always worry about foot caught in sturip and away she goes. i rode her before i bought her and the owner road her to. but i walked with her trotted and she moved and turned everytime i asked her.. i get her home gave her a few days to get used to new place and other horses then took her for a ride.. 1st time she would not listen for crud. owner told my i had to use a wonder bit on her. so i went and got a wonder bit. next time she did okay sorda. she really wanted to stay but got her out and rode a bit 30-45 mins when it was time for home she knew where that was and was in a hurry to get there.. had to keep telling her whoa but not really working to well. her buddy usually goes riding with us but still have same problems. now in the pen she is a witch!!! kicks, bites you name it to the other horses especially at feeding.. but we have 4 mares, mine which is 4-5yrs  then an 18 yr tenn walker and a 14 fox trotter due to foal in april . my horse and her friend  american saddlebreed came from the same place but she stays away from the mares they get pretty mean with each other!! when we ride she will nip the other horses if the get to close to her and if they are behind her she will try to kick which is scarry when i'm on her.. she just seems like a different horse then when i first seen her. am i being to nice not rough enough or what. her owners told me to be very gentle and talk softly to her............uumm not working. she looks at me like i;ve lost my mind.  now when i'm out with all the horses she comes up to me i pet her rub her down but god for bid another horse gets to close she runs them off. i;m not sure if this horse likes me or not.. hope some one has ideas..