I drove a semi for a while and lived by truck stop amenities. I have to say - some of their shower stalls are actually really nice. Loves, Pilot, Flying J were the ones I usually stopped at. TA and Petro are a couple others. I didn't like dealing with Petro and TA, though. We got a fleet rate at the other places and the usual was every 50gal of fuel (or more in 1 transaction) you get a free shower. I had upwards of 15 shower credits available at one time at one of the places.
Back to the root of the question at hand, though - if you don't want to stop at any "facility" (camp ground, truck stop, gas station or fast food joint bathroom) and do a shower or a "bird bath" at the sink - my suggestion is baby wipes. I've been using them since I was in college to take a "back woods shower".
When the weather gets cold I leave the pack of wipes in my sleeping bag so it can warm up. If I am backpacking/snowshoeing below freezing the pack stays in my coat or somewhere else where it won't freeze.
When it comes to clothes I do the same thing with the sleeping bag - I put my clothes in there to warm up before putting them on, if they aren't already in the sleeping bag.
I also second the motion of the sleeping bag liner to keep the sleeping bag clean. Many years ago I made a fleece liner for my 0deg down sleeping bag. It is my regular sleeping configuration. When it is mild all I use is the fleece liner as a "warm weather" bag. If it is cooler I set the liner in the 0deg down bag (all I use all season) and start off with the bag open, then cover up however much I need to for temp regulation. It works well for me.
Something to think about, also, with respect to water, is Katadyn makes a gravity-fed water filter system that uses a hanging bag. It has been a blessing for me on trips. Gone are the days of pumping water. Just fill this up and open the valve to get water. The one I have holds 10 liters. It has been absolutely fantastic. One of the options you can get for it is a shower "adapter". It is a plastic cap that goes on the bottom of the bag where the filter is that lets the water come out several holes like the nozzle cap on a watering can for plants. I admit, I have not used the shower adapter but I do have it.
The black "can" hanging from the hose is an additional carbon filter. It has black gravel in it, like the size, or smaller, that you line a fish tank with that is a type of carbon. It improves the clarity and flavor of the water - extra filtering. I like it. Again, it has been a blessing to have on trips. I can remember way back sitting at a stream with each of us taking turns pumping water to fill up a single nalgene. No more. Just fill up the bag, hang, and open the valve. Now, it does trickle water out, but that is what camp chores are for - go do something else for a while and come back.