Is there a fairly simple way to precipitate Sodium Hypochlorite from tap water before I distill it? Or, second best, a way to neutralize it?
Sodium hypochlorite is not carried over into water by distillation. Instead, at high (~100°C) it decomposes, primarily to sodium chloride (i.e. table salt) and oxygen gas, but also possibly to trace amounts of chlorate.
You could neutralize the hypochlorite by mixture with stoichiometric amounts of hydrogen peroxide, which cause immediate release of oxygen gas, a reaction which occurs even at room temperature.