Home Improvement Questions? Ask a Handyman for Answers
I can tell you a little trick that works for me. It's the water in the line from the hot water heater to the faucet that you will get first when you turn on the faucet. To ensure that this water is warm, you would have to run it and "store" hot water in this line for a short time.
So - you can brush your teeth before you shower. Run the water until you get hot water and then you will get hot water right away from your shower faucet when you turn it on.
Be sure that you don't flush the toilet or do anything else that uses cold water until you have showered.
If you can afford it, you can also get a "point of use" hot water heater. It's a small (about 10 gallons) hot water heater that goes under the sink or in a closet. If this is stored in your bathroom with not a lot of pipe between it and the faucet, you can have hot water in no time.
I hope this helps.