1. Be sure that your shut off valves are fully open going into the tank and all valves that lead to fixtures.
2. If you have old iron pipes, you could have iron debris blockage in a shutoff valve. Turn the water off and start with the valve closet to the problem fixture (in this case the bath tub). Check it for blockage. If possible, have someone turn the water on while you catch it in a bucket to check the pressure and release any iron deposits that were trapped by the valve. If the valve was blocked, you may need a new one. If this does not work, go to the next shutoff valve and repeat this until you either find the blockage or get to the hot water tank. It is possible that it is the cold water valve to the tank, however valves before that should not matter if you getting good cold water pressure. It is easy to isolate the problem by tracing the water lines and use the process of elimination.
3. In rare cases, hot water tanks can accumulate enough sediment to cause partial blockage. This can usually be assessed by opening the hot water tank drain with the water pressure on and seeing if there is low water pressure and debris in the water. In this case, flush the hot water tank thouroughly.
Mr. Fixit, November 2005