An element in household bleach that also may be present in drinking water?

Chlorine.

A molecule of chlorine has the ability to disproportionate in water. That is it simultaneously oxidises and reduces.

Cl2 = Cl-Cl = Cl^(-) + Cl^(+) Disproportionation).

Cl2 + H2O = HCl(reduced) + HClO(oxidised).

At a water treatment plant, chlorine gas is bubbled through water, in order to act as a bacteriocide, so the water is drinkable/potable.

Household water contains minute traces of hydrochloric acid(HCl) and hypochlorous acid(HClO). It is the hypochlorous radical 'ClO^(-)' that is found in bleach. (NaClO or Ca(ClO)2