I'm not saying what sokoloff said is wrong (or doesn't work) but I'd not invite a woman (or a person) to coffee before getting a physical approval. This physical approval (eye contact + smile) is usually a certain indicator of interest. I'm talking about same level co-worker.

I'd not go with a co-worker that I have power on (like being the direct manager, or the VC). I can see many ways where the relationship can go awfully wrong.