This may be over simplifying it, but when we lived in the Philippines we would just heat up some water in a kettle as-needed (via propane stove.) For showering we used the
Tabo method: mix the hot kettle water with some cold water in a bucket and use a pitcher to pour it over yourself. Same thing to wash dishes except a different bucket.
It was supposed to be a temporary thing, I was certain I would need to get an on-demand hot water heater at first but found that I actually preferred it. It uses so much less water than an overhead shower and works just as well.
Plus, you probably already have a stove and kettle, (we got the largest one we could find from a restaurant supply store) but you could also just use a pot.
For our off grid camp here in the states we're going to do the exact same thing.
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