There's a weight vs. comfort equation we all have to consider. I think there's also a grossness vs. convenience equation. I've washed my bike clothes in the shower with me, in the large pot of my mess kit, and in laundromats. All are a hassle. I've also worn my bike gear several times before washing it. Sure I probably smell gross to others, but do I care? Yes and no.

My preferred method is to wash my bike clothes when I'm showering, hang them up in camp, and in the morning if they're not all the way dry I drape them over my load on the rear rack.

Second is to stop at a laundromat, usually on a day with a short ride, and wash everything except the stuff I'm wearing. Then I wash that in the shower that night.

If there's no shower at the campground when I need to wash something I just wear them dirty the next day.