[k1vsk]

You'll need to include the plumbing as well as that is more often the source of the problem or at least a major contributor. Household bleach is commonly used improperly to treat water but in your case, it might not be a bad idea to do it once as long as you flush it well before it has time to attack the aluminum - less than 12 hours and you'll be safe. Just don't do it often. Make sure you fill the tank(s) and all plumbing and keep the pressure on during the treatment interval to ensure the entire system is exposed. Afterward, flush until no bleach smell is evident. The trick to preclude recurrence is to cycle through the tank water often so avoid stagnation.
Bleach will only kill bacteria, not viruses, so beware this isn't the cure-all it's commonly believed to be. It also has essentially no residence time so its efficacy is lost over a short time. Peroxide is safer, more effective, has a longer residence time and probably cheaper so that option is a no-brainer. Store bought peroxide is useless in this application as its concentration is too low - you need 26% or stronger peroxide to be effective. This is its biggest drawback as peroxide at that concentration isn't dangerous but is only available from chemical formulators.