Am I doing the right thing with this shy/introverted girl?

[Johnny]

There's this girl I like who seems rather shy or introverted (not attached to her friends, looks as if she were on her own world some time), that's been staring at me for quite a time now.
So I grew a pair (I'm pretty shy myself), approached her, talked to her nice and easy (college stuff), and left. Then I saw her staring at me again, I slightly winked an eye at her, and she waved at me.
Now, even though we don't share any classes, I have done a little "investigation" so I know how to "casually" run into her again, and again.
What I'm thiking is doing those short nice conversations with her for a while and (if she seems confortable and interested) "sadly complain" about how we only see each other when we bump into each other, and see if we become friends on Facebook or something like that.
Does this sound good or is it kinda slow?
Please, I don't wanna blow this up!
Thanks!

[Joe]

I wouldn't develop a "plan," You need to be sincere and spontaneous in every moment with all people.

[Carlton]

Don't ask for her Facebook unless you have to. Ask her for her number and text or call her to go hang out with you.

[Loveboo]

Just ask for her number