Invest in an electric pump that can fill a container from a stream or lake. That can be special hair washing water. One 5 gallon container would be more than sufficient.
Get a plastic pan and a pitcher to be used for hair washing. It would be okay outside if away from lakes and streams. Use biodegradable soap.
A happy woman makes for some great traveling. Might as well use a solar shower while you are it.
It still amazes me that people think living in an RV should be like a hotel. The roots come from camping. Simple solutions are the easiest and most dependable. This is a perfect example.