Toggle is right . . .
probably if a scientist with sophisticated measuring equipment was able to study this he might find a small difference due to heat radiating from the supply pipes or some other factor, but it would be so small as to be entirely inconsequential and have no impact on your bill. Basically, you're heating a certain amount of water (the water which actually exits the shower head) to a certain temperature, and that will take a certain amount of energy.
probably if a scientist with sophisticated measuring equipment was able to study this he might find a small difference due to heat radiating from the supply pipes or some other factor, but it would be so small as to be entirely inconsequential and have no impact on your bill. Basically, you're heating a certain amount of water (the water which actually exits the shower head) to a certain temperature, and that will take a certain amount of energy.