I wouldn't call that 'bullying' you in the very least. From her point of view, there's no reason she should allow you to do this & she has made it clear she doesn't want you to touch, but you didn't 'listen' so she had to 'shout' & punish you for it.
On top of that, sounds like you are a relative stranger to her & it's unclear but talk of being 'at pasture her whole like' I'm guessing maybe she is also relatively unhandled. It's lucky sounds like it was only a light warning bite, not a serious one, or a kick. And yes, if this caused you to stop messing with her leg, even for a second, &/or there was nothing in it for her, no reason, in her eyes, to stand & put up with what you were doing, then you're right to fear she is very likely to do it again.
So... First & foremost, your safety first. If you can't find a way to administer to her safely, don't do it!. If her injury is bad enough that she seriously needs the 'medicine' on it or it will be infected/get worse, then I'd talk to your vet about alternatives, &/or find someone with a cattle crush, so you can put her in, to safely force the issue.
Yes, if her behaviour was successful in getting you to quit hassling, &/or it wasn't instantly punished strongly enough for her to seriously fear that punishment in future, she will do it again & in other situations, when she feels she has to 'shout' to be listened to.
It being a dangerous behaviour, I wouldn't just ignore it, but I'd seriously punish her the instant she threatens to bite or kick at you. But it needs to be INSTANT punishment(or don't bother, it's too late), & remember, punishing something like this is a bit of a 'bandaid' first aid measure - it is not likely to be effective long term without other measures & is not going to teach her what TO do.
I'd be using 'clicker training' principles to teach her it's ok/profitable for her to put up with stuff she doesn't want you doing.