Hi sau4u,
Sounds like you have the 4-way Anderson Valve. If you set it on TANK, you can fill the fresh tank directly, without going through the water heater. But, the check valve built into the water inlet connection requires some water pressure. So pouring the cleaner in won't work. If you set the valve to SANITIZE/WINTERIZE, you can drop a short hose into a bucket of bleach solution and suck it in through the water pump. That'll let you run the bleach solution through the water heater (unless bypassed) and through to the kitchen, bath and other fixtures.
To get bleach into the fresh tank, you either need a pump to overcome the pressure requirement of the check valve, or you can empty your water hose and refill with some bleach, then reconnect it and use the campground water faucet to supply pressure and push the bleach into the fresh tank - with the 4-way valve set to TANK.