Why don't you start by saying "hey" if you are waiting for a machine she is using, or something. There isn't anything creepy about a casual hello or conversation every now and again. Or you could bite the bullet so to speak and walk up to her directly and say something like, "hey, I've been noticing you around the gym lately and wandered if you'd like to get some coffee sometime?" The worst that can happen is that she says no and the slightly awkward feeling of being rejected, but if you're well centered mentally, than you can just brush it off as it's not the end of the world. It's just a little "nah, not interested." It's not like she literally made a spectacle out of you in front of the whole gym.

Good luck!