Girls: is this too silly a thing?

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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).