Hi,
I'll give you some alternatives & principles to think about, as I largely disagree with suggestions so far. I don't ever want my horses to even suspect I might kill them, or even maim them, for 3 seconds or otherwise. I also don't want to get into a 'dominance game' with a horse either, as I don't want the chance of losing... fingers, games or otherwise, and don't want to have to repeat the games ad nauseum. Horses only tend to play 'dominance games' with others who are 'players' and are on a similar level to them. Eg. those who are true leaders don't tend to play these games. Those that do are always at risk of losing their position.
I use mainly behavioural and also 'clicker training' principles(tho don't use a clicker). You can learn the basic principles of behavioural psychology from some of the better 'clicker' sites. It's pretty straightforward & not at all as daunting as it may sound. There is also a fantastic little book called 'Don't Shoot The Dog' by Karen Pryor, dolphin trainer at SeaWorld and founder of 'clicker training' method, that I highly recommend(not a dog book, applies to any species).
Basically, as far as the training is concerned, I would be teaching her manners, yielding and to 'respect' my space first & foremost. Making tasks easy, clear and rewarding helps not only to teach the horse 'commands' effectively but develop in her a good attitude towards doing what you ask. She learns that it's the easiest option and it is worthwhile doing, because she is rewarded with Good Stuff.
Some keys to training are;
-teaching in short, easy sessions;
-breaking tasks down and progressing in small increments; -*instant* consequences *at the time of the behaviour* you want it to effect, or at worst, *within* a second or 2 of it ending - 3 seconds after the event is too long for a horse.
-Providing positive reinforcement(reward, Good Stuff) frequently for 'Good' responses. Anything that is convenient, able to be given in a timely manner, that a horse truly desires at that time is appropriate. Food treats are a generally powerful positive reinforcer. A good rub or scratch in a favourite spot is often effective.
-Avoid punishment wherever possible, use it judiciously, with excellent timing and learn the 'side effects' that come out of it, in order to minimise & address them. Be aware of what your behaviour is saying to the horse & say what you mean - eg. is retaliating in a 'dominance play' really seen as punishment, or as you wanting to indulge in these games with the horse??
-Make sure the desired behaviour 'works' for the horse - it gets her what she wants, be it positive or negative(removal of pressure) reinforcement, and that the undesirable behaviour NEVER works.
So, hypothetically, what I'd do in your situation is perhaps start on the other side of a fence, with a bossy horse used to getting what she wants. I would teach her to keep her nose to herself first & foremost, and not 'mug' me.(I teach horses to take one step back & 'tuck' their nose down to get what they want). I would stay in a safe environment like this, that I could stay out of harms way & just ignore the behaviour & ensure it never works, until she was reliable about 'respecting' my space & showing some 'manners'.
I would then start teaching her 'normally' ensuring she gets sufficient positive reinforcement & short, easy enough sessions to enjoy your 'games' and want to try for you. *Be aware too tho that 'dominant' type horses also tend to be quick thinkers & get bored easily, so it's a balancing act between making it simple enough but also interesting enough for her to be bothered.
I would strive to teach her what the Right things to do are, rather than focussing on punishing the Wrong. That is, I wouldn't consider it a regular 'tool' to be used, would think of opposing behaviours to teach her(if she's backing up & tucking her nose in or looking away, she won't be biting you).
BUT I would be prepared to defend myself if/when necessary, and try to set things up so that if she does try a dangerous behaviour like biting, she would get *herself* punished for it. Eg. if I were waving my arms, the rope or a whip around me & she came into my space, she'd get herself in the way & get hit. If I had something spikey(like a metal curry comb for eg) in my hand & she went to bite me, *she'd* hurt her mouth. Part of the reason for this sort of method is in the timing - the consequences happen *at the time of* the behaviour. The other part is about her not taking it personally, not getting into a personal confrontation with the horse, which has the effect of losing any trust & 'respect' you may have gained in her eyes.