Sounds like you have a leak on the suction side close to the pump, possibly the strainer housing O-ring if you have one. That would aerate the water as air is being sucked in when the pump is running. It wouldn't leak when the pump is off because the water would be slowly draining back down into the tank (if your pump is on top of your tank like mine is). When flow stops, it's not as much of an issue on the cold side with fewer places for air to collect, but the water in the heater would be a large collecting point for that air when it comes out of solution. That may be why you see it on the hot side more than the cold side.
