When the bus is going to sit for a month or two (doesn't happen often unless you loose your engine

), I use a bit less than a cup of bleach in the 120 gallon tank (we try to keep the tank full before we get home since I don't want to draw on our well).
We have a big box purchased dual filter system for the drinking water circuit. It takes the chlorine out of the drinking water. One time, I forgot and got the water from the normal sink faucet and I could smell the chlorine in the glass. Then drew it from the special dispenser and it smelled/tasted fine.
That does not address the shower issue, but I am not too concerned about that problem. I am sure that the concentration is much less than many swimming pools.
I would not be without the dual filter. We connect to some water sources that I think are questionable. I have a strong stomach, but I worry about Pat since we have to keep her immune system suppressed due to her RA.
Jim