Ah, an excellent question. When we have been in that situation before and needed a shower we would either hit a private campground or even in some cases a laundramat that also has showers. (These are more prevalent in small towns where there is a lot of backpacking trails. )
Many private campgrounds still let you take a shower for several bucks a person if you ask them.
If you are in the middle of nowhere and there is a lake or stream, you can always take a swim to get the first layer of sweat and grime off.
Please note that if you decide to bath, grab a bucket of water and do it at least 200 ft from the water source. Use biodegradable soap and disperse the water in the brush as you would dish water.
We always take some "wipes" along on trips when there is a good chance we'll be without showers for a period of time. That way if you want to do a really quick cleaning or something becomes irritated, you can do a quick cleaning / keep the irritated area from really getting irritated.