I'm beginning to think that the recommendation for washing out at the end of the day and air drying is probably the best solution. No more plastic bags loaded with unwashed clothes for me.
Oh, yeah, simple wins almost every time. Careful what you use as a soap and how much you use; more is rarely better. A few drop of Bronner's peppermint can do a whole day's laundry.
I don't do self-supported tours so I usually get into the shower truck wearing my bike clothes. If there's a line for the showers, I can soap my jersey and shorts and rinse them in about 90 seconds, strip them off and do another, more complete cycle on skin and hair under 2 minutes. I take much more time if there's no one waiting for a stall.
I have a mesh bag for the wet clothes. I stand where I won't spatter anyone and whirl the bag over my head. This spins out a lot of water. I roll up the wet clothes in a towel and wring it, expelling more water. the towel gives you more leverage. I have some line and a few clothespins. On Cycle Oregon we can have three days of stupid hard and horizontal rain and nothing gets dry.