I shower in the morning, dry off, shave, brush teeth, take meds, put deodorant on and then get dressed. All as one routine, if I stop anywhere in the process I'm probably not going to get finished.
Never tried to put a sports bra on while damp, although I've watched my wife try it a few times.
Drying off well after the shower then air drying the rest of the way while doing the other things seems like it works for her.
The problem I have with that is that if I sweat at night then I'm wearing that all day long. If it's bad I'll shower before bed but if all I did was go to work and come home, I'd rather sleep in the day filth, then sleep clean and carry the night filth with me all day.