Holy fuck, /adv/ I caught a serious case of feelings for my co-worker

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Holy fuck, /adv/ I caught a serious case of feelings for my co-worker and I need help. She's pretty new at this place and she's got a reputation for being shy and quiet and such, doesn't really talk to people. I didn't really understand why people were saying this, because whenever I'm near her she always smiles at me, or stares at me and brings up awkward conversations. She doesn't say hi like a normal person which was offputting at first but I figured it's her style so whatever.

Anyways, a few weeks go by and she's getting more friendly with me, when we can at least, there's rarely a time for us to just talk. But simple small sentences here and there back and forth. She smiles at me a lot and I love it, she just has this vibe and this personality that I love. (Doesn't hurt that she's gorgeous too) although I have noticed on a few occasions where we walk past each other or something and I try and make eye contact and she doesn't even look at me or say hi.

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Do you guys think that it would be a good idea to line up my break with her break and ask her for her number? I've never really done anything like that before so I don't know if it's cheesy or not. But damn it, I don't usually pick up these sort of signs. Maybe I'm blinded by my own feelings, that sure is a possibility that I'm reading too much into it. What do you guys think? I'm also a pussy when it comes to talking to girls I like, even though I am very social towards other people.