Glen is an advocate of a little Bleach in his soak sink,granted very little.I do not have a dedicated sink so for several years I scrub all my stones with comet Gel cleanser which contains bleach,rinse very well and let dry.I have never seen algea growth or any effects on the stone from doing so.
When you hone, some stones generate slurry,thats part of the stone itself,thus they need to be lapped on occasion