You do your job and when she tries to bully you, you stand your ground and don't go along with it. Only you can let the bully get to you.

If you have specific examples, talk to your manager. If they are unwilling to help, talk to HR. Keep working up the chain until someone is willing to listen, and keep a record of what you are doing. I have a feeling that if your manager isn't willing to help, then HR definitely will. Companies are hyper-sensitive to this kind of stuff. If you file a formal complaint, the company will have to take some kind of action.

My wife had a similar situation, where one of her coworkers (who isn't her supervisor) basically told the rest of the staff "I'm just a bitch and you're all just going to have to deal with that". It's taken a few months, and it hasn't gotten really any better, but at least her manager knows what is going on. The problem is that with the union, they really can't do anything.