I echo what the other posters have said regarding dating a co-worker. Sometimes the benefits outweigh the risks when you have a real connection. I know a lot of people who have met their spouses at work (and I think that's the prevailing statistic for most couples) so it is definitely not uncommon. However, I would be sure the feeling is mutual before you make any grand gestures and that you're not being pushy because it can also go south real quick.
Don't interpret smiles and polite gestures are more than such. If you're getting the sense that maybe she's just being polite, you may be onto something. Give her some time and see if she makes the effort to seek out your company. Usually, you know when someone is interested. It's a gut feeling. And the way you write about the situation is also telling. In this particular instance, you're giving me the impression that maybe it is just politeness because this is what you're trying to negate using evidence of very simple and placating social cues (which, for some reason, suggest that she's nervous about where you're going with this). And since this is all I have to go on, I would say give this some time and see how it develops.
When or if you decide to ask her out, however, give her all the chances to say no and assure her that you're asking and not expecting anything. She might be afraid of the consequences of saying 'no' and making things awkward too. It's a tricky situation for both parties and you have to be respectful of that.