I have a relationship question for girls?

[Josh32]

So I went with a small group of people to a theme park a couple of days ago; I only knew some of them. And I met a girl, who was joining us, that I really liked. We talked about the entire time, and I definitely think there was a connection. So I want to ask her out, but the problem is that I don't have any classes with her, and I never see her in school. I am friends with her on Facebook, but I would hate to ask her out that way. I know one of her good friends, so I could ask her though I don't feel doing that is any better. Do you guys have any suggestions? Would asking her out on Facebook be appropriate? Thanks
P.S: I haven't talked to her since , we just ended by saying goodbye when we left