Tile Around bathtub. Over drywall vs. vapor shield & backerboard
Will it be used as a shower as well? If so, sheetrock is the wrong material for the surround. It's going to act as a sponge if water ever finds its way to it.

What you could do is put backer board on top of the sheetrock, then coat the backer board with a waterproof membrane (I like the Redgard product for that) then tile. Be sure that the backer overlaps the lip of the tub to the inside. 

Personally, I'd pull out the sheetrock completely, then shim out the studs and apply the backerboard to that.