I presoak the panel in question, and then do my first pass(es) with a BHB, spraying foam at the point where the bristles touch the paint; I move the foamgun so the foam is contantly being distributed along the entire length of the BHB.
I move the BHB (and any other wash medium) in short, interrupted jiggling motions so that a) there's a greater chance that abrasive [stuff] will get flushed out/away by the foamgun and b) any marring that does occur will be a short little scratch, not some long arcing one.
Rinse, inspect, repeat until the panel is pretty clean. Anything big that doesn't come off with the BHB gets clayed off with Sonus green Ultrafine and lots of Glyde lube.
The foamgun pretty much flushes the BHB clean (especially with my boosted water pressure) but I still rinse it out frequently in the rinse bucket.
After using the BHB to get most of the "big stuff" off, I switch to a sheepskin or MF mitt and repeat the process, again using the foamgun to provide constant flushing and lubrication. Before each contact with the paint I fill the mitt with wash solution and hold it shut at the cuff. When all the solution has seeped out of the mitt (or when I think it might be soiled) I rinse it out and refill it before continuing. I rinse the mitts out much more often as they don't flush clean the way the BHBs do. I might rinse a mitt many times in the course of doing a single panel (and note that this is after having done most of the work with the BHB).
I end up washing each panel several times, but each pass is so gentle that I don't get much marring (I polish less frequently than once a year).