Disclaimer: I’m not a kiruv professional.
Rabbi Wallerstein has a fantastic shiur where he discusses bf issues. http://www.theyeshivaworld.com/coffeeroom/topic/tznius-recommendation-for-women
Its more than a tznius thing, its about men and women in general. If you have time for it, then I highly recommend it. (And I saw it a few months ago, I don’t remember everything he said)
As for the part about not believing, its my opinion that for someone who takes that attitude, its not that they don’t believe but that they don’t want to believe. If she sees restriction, she won’t like it. Show her that its fun, too. Aish came out with a video for Rosh Hashana done to the tune of a very catchy song. Show her ya’alili. Theres a bit of time until Chanuka, but maybe theres a Chanuka party she can go to. Are you in Brooklyn? Maybe you can go to Ohr Naava (or a similar type of place) with her for something more fun. (The schedule is on their website, but I think they have kickboxing, dancing etc). Don’t try to be mekarev her, just show her how happy you are.
1. Sorry, I know the things I suggested involve a big commitment of time.
2. Are you in contact with her parents, teacher etc? Maybe you can tell them to talk to her without going into detail (and not to mention that you were involved)?
3. Can I contact you through the mods to find out a little about the organization?
Hatzlacha!