Wow - she sounds either A) paranoid or B) uninterested. I think the detached, "not too interested myself" approach is best. She sounds like a woman who would be easily scared off by enthusiasm.
(Which is not to say something can't happen if you play your cards right - I have a friend who can only allow herself to fall for a guy if she's convinced it can't ever work out - weird, huh?)
Plus - there's nothing wrong with just acquiring a few friends through this process - they might have some girlfriends they could introduce you to.
