Is this a stupid idea?

[Masterpest899]

We go to college together. She doesn't seem attached to any of her friends, but I've caught her blankly staring at me plenty of 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 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:
"Hey, maybe we should become friends on Facebook so we can chat a little bit (because I don't want to talk to you just if we accidentally run into each other, but this is too direct, right?)"

How can I say any of that without being dumb?

[Megan]

I wouldn't say anything about Facebook! I would probably just ask her out, or ask for her number or something!

[Jessica]

why don't you just add her on facebook & if she accepts than talk to her next time she's online