My Ds was very afraid of the bath in specific I found it was a fear of slipping, plug and water on his head. I did continue with it every night same routine straight after dinner marched in there, early on I would always get in aswell as he wasnt afraid when I was in, slowly overtime the fear of being in there alone has gone, I did find bubbles helped because he couldnt see the plug and i only took the water out after he was out of the bathroom and put a washer in the way to stop the noise.
Other than those little tricks I would say persistence has paid off. Its to cold of climate for our swimming pool here and lessons wasnt an option.
As for the hairwashing thats still an issue, but I just do it when I have to at the end of the bath and we get out.