I would rinse out a few times before adding the bleach. This is for a system with a pressure pump, but I'm sure you can adapt the procedure. It takes a lot of rinsing so you want want portable electric pump for this. You can get a 110 volt version at the hardware store for not too much money.
Turn water heater off at the breaker before beginning. Do not turn it
on again until entire recommissioning is complete.
1. Prepare a chlorine solution using one gallon of water and 1/2 cup
Clorox or Purex household bleach (5% sodium Hypochlorine solution ).
With tank empty, pour chlorine solution into tank. Use one gallon of
solution for each 5 gallons of tank capacity, which results in 4
Ounces of bleach for 10 gallons of water.
2. Complete filling of tank with fresh water. Turn on every faucet and
allow water to run until what's coming out smells strongly of bleach.
3. Turn off faucets--but do NOT turn off the pump...it must remain on
to keep the system pressurized so that the solution remains in the
lines. Allow to stand for at least 3 hours, but no longer than 24
4. Drain the tank through every faucet.
5. Refill tank with clean fresh water and drain again through every faucet.
6. To remove excess chlorine taste or odor which might remain, prepare
a solution of one quart white vinegar to five gallons water and allow
this solution to agitate in tank for several days by vehicle motion
(iow, go sailing and tack a lot).
7. Drain tank again through every faucet, and refill with potable water.