How do I ask a girl from the gym out for coffee?

There is this Chinese girl, in the gym I see every weekend. She not exactly drop dead beautiful but she's pretty decent looking. We've spoken a few times and she seems sweet. The thing is, we're both sweating, on the stepping machine, burning our fat, is it the right to ask her if she's interested in coffee later? So far, one of us are already sweating when the other walks in the gym so to go for end together doesn't seem possible.

I think she's not seeing anyone right now because, in our conversations we've had she has said she's spends her weekends reading in her apartment after working out and works in the evening in a restaurant.

I'm a shy type of guy. I'm not exactly suave with the ladies... I've had opportunities in the past that I've recognized but failed to act on. I'm not asking for sure-fire pickup lines I can use on her but just the fact that asking a lady in a gym doesn't seem right..

ANyone help???