When chlorine (Cl2) is added to water it forms free chlorine as HOCl (hypochlorous acid), which is an excellent bactericide.
However, chlorine alone is not the whole story. Most liquid bleach (sodium hypochlorite) contains over 90% caustic soda (sodium). Because of this, as more liquid bleach is added to the water, the pH is driven higher. Raising the pH of the solution results in lowering the amount of chlorine that is available as HOCl (hypochlorous acid).