I got a membership at a nearby health club and shower up there.

I used to shower every day when I got home too. Lately I've stopped doing that, only showering in the morning now. I find the sweat from bike riding is different from other sweat from working, or even just sitting still sweltering on a muggy day.... It seems to be much more like pure water that just dries off. Not as grimy/sticky/stinky as other sweat. Meaning that it may not be that bad just going for the sponge bath.