One Bucket Method Power Washing
The one bucket method using a power washer to wash off your mitt or rag between panels kinda works. I'll explain.
Most of the dirt is washed away as long as it is not too deeply embedded in some kind of cloth. Dense mitts with lots of fibers, like The Rag Company Cyclone or Meguiars Microfiber Mitt were not the best at releasing dirt, because they are microfiber and designed to trap and wrap up contaminants. They are safer for your paint if your were to use them for longer than a regular sponge, because of this nice ability that takes in and buries the particles. Something sponge like and more rigid in structure seemed to be better at washing the contaminants off of it, because they were not held very tightly in the structure of the sponge by any threads of any kind. If you use a sponge and frequently power wash it out, you would have a low chance of scraping already collected contaminants on the paint.
Not all contaminants came completely out of any washing media. These things are designed to pull off contaminants from your car and trap them in their structure so you do not damage your paint. While this is good in many cases, it is not perfect or absolute minimal risk as many people strive for.
The Best Way To Avoid Contaminants Being Reintroduced
If you were to use a new rag or mitt for each panel, that would guarantee the absolute lowest chance of dragging more contaminants across paint, because you would be discarding already collected contaminants entirely in each piece of whatever you used to wipe the previous panel down with.