My stone has gotten slimy for siting in the water with wood dust and curls. Can a little bleach be added or would this mess up the stone?
Just abrade it a little bit with the stone grader. I wouldn't add bleach.
That slime buildup is algae. You can go to any pet store and pick up an algaecide used in fish tanks. I have used this without any ill effects on the stone as the chemical in this additive is safe for fish. It works quite well.