Why have we lost hot water out of the bath faucet?

Why have we lost hot water out of the bath faucet and not in the sink next to the tub?

Do you have any water coming out of the bath faucet? If not check for a closed valve. Also check if your pipe is frozen if the temp is below freezing outside. If you do have water but it is cold it could be the shower valve assembly went bad. Usually there is access from behind the shower. Feel the pipes if you can for the presence of heat before the valve assembly. You might have to do some detective work following the pipes back to where they branch from the sink and look for the problem.

I am not a plumber so this is just guessing, but ...
Do you have the type of tub fixture that has one handle that you move to control the mix of hot to cold water? If so something has become clogged in that particular part. Just a guess.

If your water is heated by gas - check the furnace and be sure the pilot light isn't out.