I bring a small dry towel and a clean shirt & bra. I wait 10 minutes, then dry off and put the clean shirt on.

If I don't wait 10 min, I'm still sweating when I put the clean shirt on. May as well not bother.

I find that I don't need water, if I have stopped sweating when I dry off. It's not that I'm lucky to have sweet smelling sweat--honestly I smell like cat piss when I've been sweating. But once the sweat has dried I don't smell, maybe the shirt sucks up all the odor because the shirt sure smells!