Bullies can't be bullies when they are alone.
If you work with a bully, this is all you need to know. They need you.
A bully is someone who uses physical or psychological force to demean and demoralize someone else. A bully isn't challenging your ideas, or working with you to find a better outcome. A bully is playing a game, one that he or she enjoys and needs. You're welcome to play this game if it makes you happy, but for most people, it will make you miserable. So don't.
The way to work with a bully is not to try to please her or to question the quality of your work or to appease her or to hide from her.
The way to work with a bully is to take the ball and go home. First time, every time.
When there's no ball, there's no game. Bullies hate that. So they'll either behave so they can play with you or they'll go bully someone else.
Call her on her behavior (not who she is, but what she does). "I'm sorry, but when you talk to me like that, I'm unable to do good work. I'll be in my office if you need me." Then walk out, not in a huff, but with a measure of respect for the person (not the behavior).
This is a shocking piece of advice. It might even get you fired. But it will probably save your job and your sanity. Most bullies are deeply unhappy and you might just save their skin. If you're good at what you do, you deserve better than a bully.