To the OP:
Great advice from everyone so far but let me add this. I realize on this site it's about not playing the sh!t games women like to play. But in this case practically every place I've ever worked there has been a chain of command. In any organization, if you go high enough, you find one person who has the authority to call the shots. He or she doesn't do it all thus they delegate, thus the chain of command. If I, as a manager, found someone else is hosting meetings where they demand info of you, what you're working on, what your workload is like, without informing me first or at the very least copying me on this, I'd blow a fvcking fuse regardless if it's a woman or not. You do NOT go around ordering other people's staff around as if it they were your own.
So, serious question, is this woman a project manager of some kind who is working on something that coincides with what you do or might pick up something in the future that could include you? That's the only conceivable reason I could see for needing a one on one with you. And that brings me to the other point - don't even go to a one-on-one with this person or any person ever who tries sh!t like this. For all you know, the meeting starts out fine, then she decides to blackmail you for something, threatening to go to HR saying you sexually harassed her. If she's a pro at this, you're screwed. The point here is if she keeps this crap up wanting a one-on-one, either make yourself unavailable and do not go but if she persists, invite or otherwise drag someone else in there with you as a witness. Does not matter who, preferably an HR rep if you can get one but another team member you can trust works fine to. Make up some excuse why you thought they needed to be there.
You've already indicated this person will backstab or connive her way however possible to achieve what she wants so do not trust anything she does.
Lastly, this advice is universal. It applies to anyone, not just women.
