Honestly, I would continually be coolly polite and professional. She seems to thrive off of drama and if she thinks you are trying to "make amends," she thinks she has the power to drive your behavior and/or actions.
I think it's nice to want to get along with everyone, but especially at work, don't buy into these sorts of nonsense games. It seems like others have her number, too.
There is a woman who is part of my working group. We have 5 sub-groups. She was assigned to group A then was unhappy with the job so reassigned to group B. Unhappy with that work so assigned to group C.
What is obvious is that she will not work as part of a group that contains another woman she perceives to be her equal in terms of intelligence and attractiveness.
I support 4 of the sub-groups and work closely with the fifth. In each group, she has managed to alienate at least one member. And the men are not so obtuse as to miss seeing her behavior.
(even though they are Sheldon-like engineers)
When this woman was initially assigned to our larger working group, she tried to undermine the authority of the Overlord (ok....retired Marine pilot with a lot of shiny stuff on his uniform)
This woman would contradict the Overlord's directions when the entire group was in a meeting chaired by the Overlord. She thought that, because both her parents had been Marines, she could treat the Overlord as a lackey and the rest of the entire group as slaves. She was badly mistaken.
Her reputation has grown over the years. No one in the entire (large) government complex wants to work with her, respond to her emails nor take her phone calls.
She thinks it is because she is so very beautiful and intelligent that they are afraid of her.