I dump the dottle right away and scrape gently, run a pipe cleaner through it, back and forth a bit, then fold the same pipe cleaner in half, to make a sort of loop, and use that to rub the inside of the bowl. I also usually use a little saliva to remove any indication of rim charring that I see from lighting. Then once the pipe has cooled, I remove the stem and use a pipe cleaner to clean the mortise and tenon, and run a pipe cleaner through the whole shebang again once assembled.
I do a deeper clean of the shank and stem with a bourbon/everclear solution every ten bowls or so, being very careful of course not to get any of that on and of the outer surfaces that have a stain on them, as it will remove stain instantly, and also not to use it with any acrylic.