When underway, the engine heats the hot water tank, which causes expansion in what is a closed water system. In my case, I kept finding water in the bilge under the hot water heater when I started out with cold water in the system. Not a lot of water, but enough that I wanted to chase down where it was coming from. Other than the bilge under my packing gland, I like the bilge areas to be bone dry.
Turns out that the relief valve on the hot water tank drips slowly as the water heats until any excess water is discharged, then it stabilizes. I now have a hose on that valve that drains into a plastic jug, which I empty as needed. I've also learned that if I leave the water pump off and open the kitchen faucet, I will develop a steady drip while I'm underway until the water if fully heated. Then it slows or stops. I put a catch-container under the faucet and usually catch about a quart of water if I'm running long enough to fully heat the hot water tank.
What that could mean for you is that the water pressure could be building up in your system and there is a loose connection somewhere in your shower line that is serving as your "relief valve". One thing you might try, just to test that theory, is to go on a run long enough to heat your hot water tank, and do it with your water pump off, your kitchen sink faucet open, and something to catch water that may drip out of the faucet (so that you know how much you are getting). If you do get water dripping out of the faucet, that will tell you that you do have enough expansion in your system for the water to seek a relief point. Then, check the shower. Dry? If so, I'd be looking for some connection in the shower plumbing that isn't tight enough to hold as that expansion pressure builds.
But you still want to consider where and how the water will find a relief point as it heats underway. Maybe the valve on your hot water heater is stuck shut? Maybe add an expansion tank? Maybe routinely use an open faucet method while the water heats underway?
Hope some of that is helpful. Good luck!
Gini