My nearest self serve wash has signs saying no bucket washing.
So I show up with about 10 cotton wash rags already damp with a little of my preferred soap on them. I'll bring them in a plastic bag that I can hang on the wall. I'll wet the car down, rinsing all the surfaces very well.
I then use each rag on a particular section of the car. One for the roof and trunk, one for the hood, one for each side (upper/lower), rear and front bumper, and the wheels. I'll mark the rags to identify the ones that are used on the wheels, lower panels, and bumpers exclusively.
I work it around loosely (not pressing), just enough to get the dirt unstuck from the surface. I'll then give it a good rinsing again, using a clean, unused rag (with no soap) to wipe any spot areas that need a little more attention.
At that point, you can dry it using whatever preferred method you normally use.
I will rinse the rags out separately when I get home, then put them in with other cleaning rags to go through the washer.
This works well for me in that is costs me about $4 of self wash bay use, cleans without causing paint damage (swirls, scratches, etc.), goes quickly, and does not break the car wash rules.
