Most Helpful Girl
I was that very shy girl. Here's what I would do. Notice what she drinks. Buy one for her, put it on her desk. She will look up. Give a wink and a great big smile, then turn around and go back to your desk. She what she does. It might take a couple more times of doing this, then ask her name when you drop off the latest drink. When she tells you, say "Hi ____ ! Nice to meet you! Stop by some time if you're in the neighborhood." That way you are breaking the ice. Then eventually let her decide how to proceed. Shy girls will be suspicious if you come on too strong too fast.
Most Helpful Guy
not to burst your bubble, but the girl could be socially awkward/disinterested not shy. There is a difference, some girls just aren't into dating, sex, etc. I know my sister and cousins are like that , also even if a girl is shy she will give you subtle signals, like looking at you ( she will look down or away when you look at her). If she ignores you that doesn't mean she is shy..