The only thing I wash daily is my shorts and maybe the jerseys. That can be done in a sink in about five minutes, then thrown on the rack to dry while riding. (This requires carrying two sets of course.) Everything else gets cleaned in a laundromat every 7-14 days.
If there was no water where I was camping, I would not bother washing at night. Wherever the next water stop is the following morning, I would wash my shorts and go. If I had some aversion to laundromats, I would do full laundry when I had access to water, using either a sink or a bag as described in previous posts. Unless you think you'll go day after day camping without access water, I don't think it'll be that big a deal.
also this:
Originally Posted by
staehpj1
I would suggest that stealth is not required on the Trans America. We stayed for free more often than not without any need for stealth. It is your call, but why not just stay in places that have water when you can do so for free?
I've only done about two weeks on the TA, but we stayed in churches for free for about half the nights. My friends who rode the whole thing said that it was the same for the rest of their trip. They got most of their leads from the Adventure Cycling maps.