... do you have any flexibility in your gym schedule? Is there any way to just start being there when she is not, and not being there when she is?
(Won't work if you're taking the same workout classes like T'ai Ch'i or spinning, I know. But if you're just there to do sets, it might work, if your schedule allows. And yes, I know what an upheaval this would be. I had to do it myself, long long ago, switched from after work to before work. It was extremely annoying, but far less annoying than the pest I avoided.)
Also, be-very-ware of compulsive liars, who never let you get a word in edgewise, and who are the center of their own little personality cult where everyone thinks they are wonderful *because* they're constantly telling everyone how wonderful they are. These are the hallmarks of the common or garden variety sociopath, and they always turn nasty, and when that happens their worshipers are often eager to join in.
(If you cannot avoid her, the Gray Rock technique might work. Be dull, dull, dull and don't react or respond other than perfunctorily (but politely) - definitely don't open up about anything, no matter how much she confides or tries to impress. If you can be consistently dull, flat, boring, without antagonizing, she'll lose interest and go after tastier prey.)
Sorry you have to deal with this.
_________________
"I believe you find life such a problem because you think there are the good people and the bad people," said the man. "You're wrong, of course. There are, always and only, the bad people, but some of them are on opposite sides."
-- Terry Pratchett, Guards! Guards!