My tablet decided to run out of battery power before I could post my reply. Argh. So I'm trying again, at my desktop. Power company, don't you dare fail me now!
To the posters in general: Thank you for your perspectives. They give me some interesting things to think about. Also, something that I should have put in my initial post: this woman made me cry twice with her vicious comments. After the first time, I realized she was not truly a potential friend, and backed the EHell away from her.
Boss and BigBoss know about the second time; Boss actually witnessed it. Coworker has been written up for this. She thinks that because she apologized, everything should be all right between us two. It isn't. I know I can't force her to understand that. She wants my regard and my attention, but I have none for her. And I do want to discourage her from hanging around me.
By the way, yes, I now document my interactions with her, no matter how benign they are. Just thought I would throw that in there. There is no HR department to worry about; it's a small business of 30 people, so I'm not worried about HR. But documentation might come in handy if I ever need to justify myself later.
camlan: I will keep that in mind if Boss or BigBoss ask me to be nicer to Coworker. During the meeting, BigBoss did ask her to be more specific. So did I. Coworker wants me to paste on a grin when I greet her or if she needs to come to my office about work-related stuff. I am currently pondering if that is a reasonable request on her part or not. It seems unreasonable to me but that's why I came here.
Redsoil: Yes, you're quite right. I'm being frostily polite, not pleasant. I already understand this is the effect I'm giving off. I'm concerned about slipping into actual rudeness, not so concerned about being "pleasant" to this one person.
Lynnv: Thank you. It helps to know that other people have had to deal with some really heinous coworkers too.