a btu(british thermal unit), is the amount of heat energy it takes to raise the temperature of 1 pound of water by 1 degree farenheit.
1 btu = 1054.8 joules...
if you want to raise the temperature 50 degrees,i don't know how much water is in your tub but i will use a smaller example and you can substitute the numbers later......
a tea kettle holds 2 pounds of water...
lets say at room temperature (68degrees farenheit)...not counting the radiant heat losses etc to the kettle....
the following should be the result 2x(212-68)=288 btu...and thats for a kettle,your tub is exponentially larger and i don't have the stats in front of me for the specific heat capacity of wood..i know paper burns at 451 degrees farenheit(hence the movie farenheit 451)....i don't remember what water weighs but i think it is 5 pounds per gallon or somthing like that...figure out how many gallons of water you have in the tub, calculate it's weight,use the above formula to give you how many btu's, then light wood stove...
it isn't really how much wood you need, it's how many btu's and for how long...oh and by the way....
it takes 288 btu's x 1054.8 joules =303,780 joules of energy just for a kettle...no matter if it takes a while to heat that much water for your tub by wood heat,it makes far better sense to use wood and save the electricity like you said in your post......good luck....pickster