Wierd bathroom water problem

The first thing I'd check is to see if there's a check valve in the outlet of the water heater. If you have just one valve to change to winterize, you probably have a check valve. The check valve has a small disk that blocks the flow of water back into the water heater. That disk is plastic/nylon and is held in place with a spring. I've seen several of them come loose from the spring and lodge in the outlet of the water heater. It's hard to get to the back of the water heater to get at the check valve. There's no maintenance. You must replace it. I found a replacement with a metal disk right next to ones with the plastic disk. Choose carefully.