Don't use soap for dishes. The only reason for soap in the backcountry is for hand hygiene or first aid and it should never be used near or in a water source. If you need to use soap, used collected water well away from water and ideally bury the effluent.
In active bear country choose meals that only require boiling water and eat out of the bag. Then there is no pot to clean.
Keep your pots in your bear can or bear hang. If your pots won't fit in your bear can, place you cleaned pots on top of it as an alarm bell if something disturbs the can. The can is supposed to be at least 50 feet away from your camp in a location that makes it as difficult for critters to to roll it away.
If you actually cook and need to clean a pot, don't let it sit and congeal. Clean out the pot as best you with your spoon...why I prefer a spoon to a spork. Immediately heat up a little water in it swish it around to dissolve the food stuck to the pot and drink it...you need the hydration and calories because backpacking is not for weaklings and wussies.
But seriously if drinking the dish water that is too gross, walk at least as far away from your camp, the trail or a water source as you would to poop and toss the dish water in a broad spread. If you have left over food from a meal that you will not eat, it is best to pack it out. If for some reason that is not possible bury it using the same rules as poop...consider putting it in the same hole.