The problem is ... I don't think he has a gray water tank, I think he is dumping on the ground.
I used a blue boy tote tank.. the one I had was 10 gallons as I recall.. I modified a 15 gallon tow hook so I could tow it to the dump station.
There is basiclly nothing you can do to "Clean" the tank, since you don't have one. The only waste that is held "in-system" is what's in the P-Trap under the sink, Depending on your plumbing either a half cup of bleach or some Foaming pipe cleaner would be my best suggestion on board, Followed by a lot of water..
But insted of a bucket, use a 5 or 10 or 15 gallon blue boy toat for the gray water and haul it to ye-old-hole in the ground.
Note; If you get a 10Gallon uinit the tow fork won't fit.. However I have one that will.. What I don't have is the 10 gallon tank any more (Forgot to pick it up when I cleaned out my storage locker) But I think I have the modified fork.
Home is where I park it!