" 2x6 subfloor with 2x6 joists 16" OC. "

You have everything but THE most important number.

What is the joist span from support to support?
2x6 is pretty small for joists (the 2x6 floor will ensure good load sharing though).

This post was edited by brickeyee on Wed, Apr 24, 13 at 15:21

Unless the bathroom is bigger then 10'x10' sounds to me good enough although you should loose the hardwood and have at least 3/4 or 7/8 plywood before thebcement board.

Your first option is a bad idea because you should not tile over strips of wood, which is what your hardwood floor is. It is not stable enough.

You second option might be better, or it could be just as bad, depending upon the material used for your subfloor. If your subfloor is strand or particle board - no good.

You want plywood, screwed down into your subfloor, but not into your joists.

If you are concerned about height AND want to do the best job possible, rip out the hardwood and install plywood + either cement board (hardi or other brand) or Schluter Ditra (Ditra only adds 1/8" AND provides a water barrier). You can get to exactly the height of your existing floor if you plan it properly. Use two layers of plywood if you need to.