You might want to consider one of those solar bags. I forget the name brand of it - but basically its a black bag that you fill up and lash to your deck somewhere. After a few hours of sun the water gets fairly toasty. Won't help with a morning shower obviously but its an alternative to dealing with propane. I have one and it works as advertised.
I've used those too when I used to camp and ride my 'thumper' in the desert. I would but two of them (makes 10 gal.) on the hood of my truck while out riding, then hang them from a stake in the back of my truck during a shower. The water never got real hot, but was much better than nothing in getting the day's dust off me.