You're analyzing too much. Who are you trying to be, Euphanasia?
Maybe she's humble and if you spontaneously approach her and say something like "Oh, hey, I liked your song (of course you didn't) bla bla", you might form a friendship man.
Not only does this man have a point, but you're mistaken.
Watch some sitcoms. Gyms are perfect places to pick up people. Not that I ever do it, rofl, but your notion that she wants to exercise without hassle from some random dude must be wrong. People get picked up in gyms all the time, I have even watched it happen as I myself worked out.
For some reason, I love how you put that. Although with a humorous tone, that's what it's like. Hot people are gonna have to expect extra attention, that's the way of the world. By her age Chronic, she's probably used to it by now. Bring your pigs and tell her how you took them in cause otherwise they'd have no home. She's guaranteed to perform the sex with you later in the evening.