[Mz]

If you really, truly think you are being bullied, then perhaps you should to go HR and report it. Since that seems to not have crossed your mind, I have to wonder why? And it makes me suspect that it isn't as simple as she is merely a meanie who is mistreating you and you have done nothing wrong.

And that brings me to this:

You don't necessarily need to apologize to her, but you should make every effort to show your respects to this person. Even men who mean well and are trying hard to not be sexist often fail to genuinely treat female colleagues with the same degree of professional respect they treat their male colleagues. So, assume you fell short somehow and try to rise to the occasion and get it right this time. Quit blaming her, accusing her, acting like it is all her fault, etc. Be an exemplary professional and expect to earn her trust and her respect.

Best. It sucks to have workplace friction, no matter the reason.