First approach ever:

Background: In gym, have intermediate/advanced physique and good style, good haircut, carry myself with confidence. Girl I approached has smiled at me before moved close to my vicinity and done double take looks at me before. When she walks by I may subtly smile or glance at her.

Approach: Finish my workout, she's on a cable machine with headphones in. Finishes her set. I've been resting on a somewhat nearby bench for maybe 3 mins preparing myself. Around 20-30s after her set. Go up from 1:30 angle and say "Hey". she takes out headphones and says "hi" and is clearly still flustered/out of breath from her last set. I say how are you, she says good. I say whats your name and stick out my hand for a handshake, she says sophie and shakes my hand. She's still worn out. I say something along the lines of you seem worn out, working hard, she nods like yeah no shit. I say "I was gonna go get frozen yogurt after my workout would you care to join me". and she says "I can't I have work" or "I can't I have work sorry" and looks away still out of breath. I say something along the lines of "Alright have a good rest of your workout" and walk away.

Analysis: Probably should have said I'll come back and talk to you once you catch your breath or caught her as she was leaving instead of between sets, but I was ready to leave at this point. I was also maybe too professional although confident in what I said, needed more emotion perhaps. The handshake was business like and was a weak handshake, she didn't really fully grab my hand