Well, she has a point. You started it the wrong way saying some odd sh1t. I mean, WTF, you don't open girls while they do their sets! And not with crap like that (trying to get them to smile, not be uptight). You blew it totally. Next time be smoother. Calibrate what you say. At least wait for them to have a pause between their sets.
And don't go any further when she doesn't want to talk with you. Just end the interaction smoothly:
HB: "Look. Can you work out well when someone is talking to you?"
DJ: Haha, yeah, i like to chat while i do work out. Ok, you can't, so i won't bother you more. Have a nice work out
But the situation exploded in your face. You handled that part well, like everyone has pointed out.