Sounds like you are planning on using jacketed cable, or "romex." I don't think that's a good idea for a 50 amp run. I know it makes things easier, but you end up with a smaller ground wire, and I don't think it will pass an inspection.
Go with 3/4" conduit, or 1" if you want it to be real easy to pull.
Don't mount the sub panel any closer than five feet to the water.
Add an extra circuit breaker to the sub panel for a courtesy outlet - seven to twenty feet from the tub - and make that outlet a GFI type in case your wife throws the electric rolling pin at you while you're in the tub.