Bleach is sodium hypochlorite. Just for economic purposes, water and wastewater companies normally use gaseous chlorine (Cl2). Once the chlorine is in the water (regardless of whether is it NaOCl or Cl2), it reacts with organic compounds to form chloramines. Chloramines also disinfect the water and are more stable than molecular chlorine.
So what are the major health problems people are seeing from fluoride and chlorine in our drinking water? I think it's a case of getting afraid of nothing. My teeth are healthier than ever. I haven't contracted cholera or typhoid fever. Water seems fine to me. If your health is poor, find out the real cause and stop blaming the water. Hundreds of millions of other people are drinking it and are fine.