Girls: is this too silly a thing?

[553]

She's stared at me several times (she doesn't seem attached to anyone, really) and we talked once (it was very pleasant), but we don't share any classes (we go to the same Uni).
Oh, and once I saw her and winked at her, and she waved right back at me.
Is it OK to tell her something like
"Hey, I don't want to talk to you only if we bump into each other. How can I find you on Facebook?".
Or would be too weird?
See, since she doesn't seem attached to anyone I don't want to be too pushy (sending a FB invitation without telling her) or too weird (asking her if she's on FB?).
Also, how about the part about me not wanting to talk to her just when we run into each other? Is that too direct?
Thanks! (Oh, yes, I am so clueless).

[Icecream]

I think you should ask her for her Facebook! That way you guys can chat more. I know a lot of people don't think of Facebook as popular anymore but I still use it and it works for me!! I would just ask her.

I would probably change the question to something more like "Hey, I don't see you around that often and I would love to get to know you more. How can I find you on Facebook?"

[Georgie]

Telling someone you don't want to talk to them is mean and hurtful. How would you feel if someone said that to you. Forget about Facebook. You need to talk to her face to face.Smile when you talk to her, and use good eye contact.