Asking a woman out that goes to my gym

Ok I go to this gym and I am in pretty good shape I dont bother anyone and have never talked to a woman at my gym because I know most women do not like to be hit on at the gym. So with that in mind i just put my headphones on and workout. One day i decided to try this cycle spin class and there she was and it turns out that that she is the cycle trainer! I have two problems 1.)she is very attractive so I know she gets hit on. I think I am attractive as well but I dont want to be like everyone other guy! 2.)We are not of the same race I dont know how she feels about that. I smile and say goodbye after class but I feel like she is still in trainer mood that she dont even notice me in that way,I dont want to put her on the spot. so is it best that I just leave it alone or try to be subtle and drop hints??