There's this girl....?

[John T]

Before you read this, if you plan on leaving a one word answer or such please don't both answering.
So there's this girl I really really like.
First "met" her in a lecture in the first weeks of university. Met meaning she happened to sit next to me, didn't really get to know each other by names and didn't talk all too much it being a class and all. Then never really "talked" to her again, though she would always say hi when she saw me around campus (even though we hardly knew each other!). Anyways, she is in one of my classes this year but it will be the last class we have together since we are both studying different things and such. The thing is I am way too nervous around her (and girls in general) to even say hi, let alone something smart.
This is going to sound weird but I actually look forward for the weekend being over because I get to see her in class, although not even be able talk to her.
Would it be a good idea to send her a facebook message (after the term to avoid awkwardness in class)? Since there is no way I'll ever be able to actually go up and start a conversation (pathetic, I know). Or would it be a bit on the creepy side. Or if I did send a message, should I make it anonymous and try to hint at who I am?
What I don't want to do is be that guy that she sees as weird and looks at differently.
I just want her to be a friend
If I did decide to send a message, what would I say? Just spill it all out about how I feel or just say hi?
Please include your age in your answer.
Thanks!