Should I keep not talking to her?

Personally, if the girl is telling her friends you're a jerk, I wouldn't want to be with her. Though if you do want to be with her, slowly start getting more contact. Don't rush into it, do it slowly, adding a little bit more after a while. Though don't go too far. If you want her as a girlfriend, don't fall in the Friend Trap. That's when you get so good friends, she's afraid to lose the friendship, so you have to remain friends, instead of she becoming your girlfriend.