I don't know how to talk to her

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Ok, I'm a freshman in college and there is this girl that I am really interested in. I think she knows that I like her. Sometimes I get the feeling that she might also be interested in me, like when we have class in the lecture hall I see her look around the room and when she spots me she'll sit somewhere in my line of sight. Once I saw her and we made eye contact for a moment and she blushed hard. The thing is, I can't bring myself to say 2 words to her. Sometimes when I'm walking back to my dorm she'll walk by me and I clam up, the words won't come out. So I was wondering would it be acceptable if I sent her a message on Facebook.com? I mean since it is a network for people to meet folks who go to their school I really wouldn't be misusing it but I don't want to seem weird or anything. I'm just very shy and I think "breaking the ice" without being in front of her might lift a huge weight off of my shoulders