First, Thank you for your service. Glad your injury doesn't keep you from enjoying your RV and traveling.
#1. The pressurized city water connection does not fill your fresh water holding tank. The two systems are isolated from one another.
#2. Find the fill port for your fresh water tank. You can fill the fresh tank with your fresh water (white) hose about 1/2 full. (Read your tank water level monitor inside the Cougar) Next, Mix the bleach, with water, into a one-gallon container and pour it into the fresh water holding tank. Fill the fresh water tank almost completely full of potable water. Turn the water pump on, open all hot and cold faucets and run the water until you smell the bleach at each faucet. Close the faucets. Let this sit overnight. Next morning open the fresh water tank drain valve under the trailer and drain the tank. Re-fill and drain again. Refill and turn on the pump and let water run through all faucets until the bleach smell is gone. This is usually enough to get rid of the bleach in the fresh tank but you may want to drain and refill one more time.
Here is short video that might help.
#3. Get out there and have some fun!!