Here is the key to washing dishes while using minimal water. Get a dishpan that fits sink. CW has the right size for a lot of RV sinks. Put dishes in sink and add soap. Start to add water, but also start to wash dishes as water goes into dishpan. Use just a small stream of water, and after washing each piece, rinse it in the water running into the dishpan.
Hopefully, you can get all the dishes washed and rinsed before the dishpan overflows. When you are done, all the water from washing and rinsing dishes will be in the dishpan, so take it and dump it in the toilet!! In nearly all cases, the toilet or black water tank fills up much more slowly than grey water, and all that soapy water is good for the black water tank!
Because the water I use to wash dishes is not as hot as that in a dishwasher, I also add a bit of bleach to the dishpan along with the soap. (This is what restaurants used to do before they had super-hot water dishwashers.) I usually am alone so it does not matter so much, but if I have company, I make sure my dishes are sanitized.
The other option is to take the dishpan full of dishes to the campground dishwashing sink. Please do NOT wash dishes in the water faucets in the campground, as the food particles that end up on the ground attract animals and bugs.