Transient RV parks are the ones that most likely prohibit washing. It's because folks stay on the sites only a day or two and if there was a lot of washing the ground would be saturated and thus, puddles forming in tire indentations. If the sites are concrete this probably wouldn't be an issue.
Also states that are in serious drought ration the water usage.
We've never encountered a park that wouldn't let us use a bucket. We'd wash the windshield and perhaps the door/bay areas. We didn't bother with the higher areas as they wouldn't show the dust or road grim. When you travel to Alaska you definitely need to wash the windshield daily and sometimes more than that! We learned at a truck stop that adding some windshield washer fluid in a half bucket of water gets the bugs off easily.