(Only girls) Should I do this?

[625]

We go to college together. She doesn't seem attached to any of her friends, but I've caught her blankly staring at me several times.
After a while I went to talk to her. It was nice, no awkard silences, in the end we asked each other's names and that was it.
The next day I was at the cafeteria going to my table, and I looked up and there she was, with her friends, looking at me, no facial expression, completely absent from her conversation. So I winked at her (my hands were holding the tray) and she waved right at me, blankly.
The thing is that I only see her when I bump into her, and I don't want her to lose whatever it is she has for me.
But I was thinking that the next time I see her I'll say something like:
"Hi! I haven't seen you in a while! Maybe I should introduce myself again. Hi, I'm [my name]"
"Bla bla bla"
"Listen, are you on Facebook? Maybe we should become friends on Facebook, 'cause I don't wanna talk to you only if we accidentally run into each other"

What do you think?