Zeraph

I think sometimes opening with a question, so that it looks like you bumped into her acidently is better, and then say Hi, my name is..whats yours..

Causually: (raise eye brows, dont smile) Have a good workout? pause, (then make a general statement like) I find it really helps me relieve stress. Then moving on to talk about some other form of exercise that's not in the gym that you like to do, like hiking. Then continue the convo from there and at the end ask her if she'd like to go hiking. That make sense?

Just my thoughts, I don't do this much, but it seems logical and almost risk free.

EDIT: Oh and obviously, you wouldn't do this while she was working out, but resting, and youd still want to make eye contact and smile first, etc.