I run about 10 gallons or so of water into the tank then disconnect the hose at the faucet and pour the bleach into the hose (as Scottyb said) with a glass measuring cup. I add about 2oz for a full tank of about 110 gallons of water.
Are you doing this every time you fill the tank to simply create fresh drinking water?
2 ounces of bleach to 110 gallons is roughly what the CDC provides as the guide to create safe drinking water. This will not be effective in "cleaning" the fresh water tank.
To create fresh drinking water, the CDC recommends adding 1/8 teaspoon of unscented liquid household chlorine (5–6%) bleach for each gallon of clear water. This equals 1 teaspoon for 8 gallons.....which is 12 teaspoons (2 ounces) for 96 gallons.
To sanitize (clean) the holding tank and water lines, I've used the chart below as a guideline. I will fill the tank with this mixture, run all water lines until I smell bleach, then allow to sit for 8 hours. I then drain the tank...fill with fresh water and run all lines for 5 mins. I allow that to sit for another 8 hours. Then repeat one last time....fill tank...flush all lines. This last tank (3rd) will stay in the trailer.