Tendency here is to leave shower/bath water to cool down thus
releasing its warmth to the bathroom. We always have the exhaust fan
running while bathing of course to get rid of moisture.

And while we are in the bathroom (in centre of house, no windows) six
40 watts bulbs (total 240 watts) above the vanity mirror are on
keeping the temperature comfortable so that relative humidity is not a
problem.The mirror. for example, fogs over for five to six minutes and
then clears by itself. There are no mould/mildew problems.

We have a fiberglass-shower tub unit. Hot water is heated electrically
in basement below.
A 500 watt baseboard bathroom electric heater rarely cuts in, the
lights and other warmth keeping up the bathroom temperature.

At the end of a typical shower there is warm water in the tub about 4
inches deep, 15 to 18 inches wide and about 48 inches long. These are
probably a bit overestimated; but to continue ............. that's 0.3
x 1.5 x 4 cu feet of water = 1.8 lets say 2 cubic feet of water?

Water weighs 'about' 60 pounds per cu foot. So 60 x 2 = approx. 120
pounds of soapy water at a temperature of around the human body; say
90 degrees F?
..
Leaving it to cool down for an hour or two, to say a room temperature
of 70 degrees F releases 120 pounds times 20 degrees = 2400 BTUs of
warmth.

One kilowatt/hr of electricity will produce 3300 BTUs of heat.

So 2400 BTU's of warmth requires 2400/3300 = 0.73 (approx three
quarters of a kilowatt/hr).

Our electrcity costs, on average, ten (10) cents per k.watt/hr. So; by
doing this am I saving some 7 to 8 cents per shower?

With an average of 1.5 persons in house one shower each per day = 365
x 1.5 x 0.08 = potential saving of $44 per year? Enough, maybe, for a
magazine subscription?

Welcome comments, criticism, or advice whether I have dropped a
decimal point (or other grievous error) in calcs.

And of course the above is probably a 'high' average. Many showers are
quicker than that (less used water). While, for example washing one's
hair couple of times a week, while showering takes an extra minute or
so.