This could work if you prepare the new room for the additional moisture. First, make sure all glass in this room is double-pane to avoid excessive condensation. I would also recommend a Low-E film between the panes (or applied to the inside surface) to reduce heat gain, if this room faces South or East. Depending on your budget, you might want to consider Argon gas between the panes as well, as an additional feature which will help increase the insulating value in winter months. All woodwork should be sealed, painted, or stained with quality oil-based products to keep them from absorbing too much moisture. This includes windows and doors. Prime all sides of new trim before installation. As for the walls, they will need to have an oil based, low perm (low permeability) coating, to prevent excessive moisture from being driven into the walls and rotting the framing. Finally, a good quality through-the-wall exhaust fan with a humidistat control should be placed high-up on a wall to automatically come on when the humidity level reaches a certain level. Get one with a low "Sone Rating", which is a measure of a fan's noise. A sone rating of 1.5 or less would be desirable, but make sure the fan is large enough to exhaust the size of room it will be installed in. Pay particular attention to proper electrical details to avoid a potentially deadly situation. I would suggest the wiring ONLY be performed by a professional. Don't be in too much of a huury to jump in the tub, until you get the details right, or you will see your hard earned dollars turn to mildew and rot. Best of Luck.