The last trip out for the season we use Chuck's method. During the active camping season, we will drop one of those dissolvable holding tank treatment pods down the bathroom sink drain and kitchen sink drain (we have two grey tanks) and of course the black tank too.
Bleach will kill germs, but the issue is soap/grease build-up in the tank and that needs to be digested/removed and bleach will not do that, and in fact could harm the valve seals.