like others, we add some HE laundry detergent, either liquid or power, some calgon water softener to the black and grey tanks. For the black tank we also add some of the enzyme/bacteria based black tank stuff. I don't use any bleach, can't see a reason to and am concerned it will counteract the enzyme/bateria based stuff.
Works well, even after a week or more of camping. If I dump at a dump station, I backflush at least 10 gallons or so of grey water into the black tank when I dump and let is slosh around on the way home. I have a dump station at home and all the sloshing around on the way home pretty much puts everything left into solution so it is easy to dump and clean the black tank at home.