We do the same as wyocamper. Plus is the method in owners manual.
But, (there's always a but)
Since we have an installed whole house water filter, we remove the cartridge prior to introducing chlorine. Then use the onboard fresh water pump to draw chlorinated water out of the tank and into all the waterlines.
Fair Winds and Following Seas
Terry & Rosalina
2007 Winnebago Journey 34SE
Retired Navy Mustang & Navy Wife
It's not the only way, but it's the easiest for me. You could use a funnel or an oil can with a spout to add the bleach through the gravity fill, then fill the tank and proceed with sanitizing the water lines.