It's complicated. Basically, there are three principles to understand: 1) vapor will move from warm space to cool space, 2) if and when vapor gets into the wall, and it will get in, then it needs the ability to get out, 3) we're not dealing with "moisture" from the exterior. (I'm assuming the building envelope does not leak), and 4) all this reverses for warm climates.
So, 1) is simple...sort of...just make sure you have a really good exhaust fan. Your bathroom (I'm assuming there's a tub/shower) will generate a lot of "vapor" and what does not get exhausted, will migrate into the wall...no matter how good your "vapor barrier" is or how good it is installed. When this occurs, it will turn to moisture at the dew point. Now it's a problem.
So, as 2) implies, when the vapor in the wall turns to moisture, then it needs to escape. If a "moisture barrier" (moisture barrier has a perm rating of 1.0 or better (less)) is installed on the inside face of the wall, it will inhibit the moisture from escaping. Therefore, I do not recommend installing a moisture barrier (polyethylene sheet, foil faced insulation or similar) on the inside face of the wall...vapor barrier (with a perm rating from 10.0 or worse (higher)) yes, that's ok.
3) and 4) are not discussed here, but important to understand. (Some people think no exterior "moisture barrier" should be used because in the summer this all COULD reverse. However, all siding manufacturers recommend a moisture barrier and I think too much moisture would be injected into the wall system without the moisture barrier.)
Whether you use batts or rigid insulation it does not change these concepts. If rigid is used, I'd use closed cell so vapor does not penetrate the rigid board and then get trapped.
Also, these principles are the same whether it's an interior wall or exterior wall. (I wouldn't use insulation in an interior wall, unless it's for sound control.) But I would use a "vapor barrier" on an interior wall.
Also, same principles for ceiling...use vapor barrier (no poly, etc.)
It's very confusing: Moisture Barrier = perm of 1.0 down to .01 and Vapor Barrier = 10 and up. (By the way, a really good paint system has a perm rating of 6.0-7.0)