I think the mature and assertive thing to do would be to tell her what you've found out, and then simply say that as a result, she is not the kind of person you're interested in being friends with. Don't get mad, don't get dramatic, just state your case and then move on without her.

...and I whispered to the horse; trust no man in whose eye you don't see yourself reflected as an equal.
-Don Vincenzo Giobbe circa 1700