I had not time to explain myself better before, but I do believe that the best way to heat up water with wood is using a rocket pocket! You make the rocket pocket with a metal barrel, you immerse the whole system in the water, add wood to the stove and there you go. There is no heat loss to the surroundings, to the earth nor to the air. All heat created by the stove is directly transmitted to the water (Except for the chimeney!). You actually contain your whole fire inside the water! What can beat this??? A rocket pocket works on the principles of the rocket stove which makes it very efficient, but has no unnecessary mass to heat up for this case. I have tried it and it works fantastic. If you make your bath big enough you can have your stove in it, or if not, you can immerse the rocket pocket inside a bigger barrel filled with water and then circulate the water from the big barrel to the tub. The only complication is to make your rocket pocket water tight, but you can use a barrel with a water tight lid and weld your two tubes to it. Not so difficult.
The same principle can be applied to warm up shower water using wood. I also agree that preheating the water with a solar system is a great and cheap solution.