How do I talk to this girl & get her to like me?

She is anything but approachable- home schooled in a big catholic family. I really like her. We've been friends for about a year. Not really close though, just casual friends. The only time I see her is at church. She doesn't have a cellphone and the only time I get to talk to her really is on Facebook but she isn't on very often. Youth group is over now so I don't actually get to see her. Normally I'd try the getting to be friends with her friends tactic but she doesn't have any really close ones that I know well. In fact, she wrote on my wall randomly one time and said "Matt, you're my best friend!" So I get the impression she doesn't have much of a social life. And the problem is I KNOW her parents wouldn't let us hang out alone. I really like her and we have so much in common. How do I get to know her better?