I know I know, people told me that is not a good idea but I'm into her! And after a couple compliments I think there's a chance she could be into me too. The thing is, I don't know which route to take.

Do I just keep talking to her when I can, try to throw some flirting (whatever that is) and some teasing and see where things go. I think that's the most reasonable way. Or should I just ask her out on a cool way "hey I've been wanting to visit that new place, and it would be cool if you came" this instead of an "in your face" approach.