Bathtub sizes run from 40 to 100+ gallons; that's like running a shower 16 to 40+ minutes to fill, running 2000 light bulbs the whole time.
http://www.instructables.com/id/Cozy-Low-Energy-Shower. I take a simpler approach - I hang a cut-off shower curtain above the door to my shower.
Hence, the wattage needed to continuously heat water for a normal shower is
20 kw corresponds to 2000 10-watt compact fluorescent
That 20 kilowatts is nearly as much as the total electrical capacity of many homes. The typical standard for modern homes is 100 amp, 220 volt service (see this link), or 22 kilowatts.
Installing a low-flow shower head (1.5 gpm) saves 40% of that, 7955 watts or about 800 bulbs, but it still uses 1200 bulbs worth. An older shower head may use over 5 gpm, over 4000 light bulbs.
This does not consider conversion losses (when producing electricity),
transmission losses, efficiency of a gas or oil hot water heater, or the energy cost for delivering gas or oil
to homes. It ignores evaporation - that steam from your shower comes with evaporative cooling, sucking heat out of the air in your home. Now if you're in a hot climate you may think that's good - but if you're running the air conditioner, it uses even more energy to reverse the process to get the moisture out of the air.