The TL;DR -- vapor barriers belong on the outside only
You should only place a vapor barrier on the exterior side of the exterior wall, allowing the assembly to dry back to the inside if water does get in past the tub surround. I would recommend paperless drywall over cement board for the tub surround, as well -- gypsum board of all types is vapor open (around 50 perms) while serving as an air barrier, allowing drying to the inside without letting a ton of humid air into the wall cavity, while cement board is a fairly severe vapor retarder at 4-8 perms, which puts more pressure on the ability of your tub surround to keep water out of the wall to begin with.
What happens when you try to stick one on the inside?
When you stick a vapor barrier on the inside of a building, all will seem well at first, until you go and turn the air conditioner on. Then, the moisture in the warm, humid outside air that fills the wall cavity will start to condense on the cold exterior surface of the vapor barrier (assuming an insulated assembly), and you get mold as a result.
A similar problem will happen if you try to insert two vapor barriers in the same assembly -- the inside one will still generate condensation despite the efforts of the outside one to keep all that humidity at bay, and now there's utterly nowhere for the moisture to go!
Of course, there's no point in putting a vapor barrier on an interior wall -- the airspace of a partition should never communicate with that of an outside wall!
More info on why vapor barriers are like badgers can be found in BSI-073, aka "Macbeth Does Vapor Barriers."
Popsicles are for sucking, bathrooms aren't
One other mistake that can be made in a modern, tight house is to slap a "fart fan" in the bathroom and call bathroom ventilation done. Doing that just means that your makeup air will come from all sorts of random leaks that have no business providing indoor air to people -- especially if one of them happens to be the range hood, or the exhaust of some appliance.
The easiest way to solve this problem is to provide transfer air to the bathroom from a zone that's being blown on, say the basement, if your basement is a suitable transfer air supply, as not all are! (You'll need to provide, oh, 10% extra makeup air as this is a transfer air setup, as well.)
Of course, if the OP's house leaks more air than a SR-71 on the ground leaks JP-7, an old-fashioned bathroom exhaust fan like the one the OP proposes will serve him fine.
More on ventilation in general can be found in BSI-070, "First Deal with the Manure and Then Don't Suck", by the way.
Most of the time in a house in Canada you would have 6-10mil plastic over the drywall in the ceiling.
However the answer isn't that easy and the vapor barrier isn't needed for sure.
It also depends on the type of insulation that you have (faced or not), what other types of barriers are installed in your attic, and really what is on the rest of your house.
So from this picture I would get a ladder and look at what was in the next room on the ceiling. I would do the same thing.
My personal opinion... is that I don't like a vapor barrier in the attic above a bathroom. Unless you paint the hell out of your ceiling (which I do for bathrooms including two coats of Killz oil based primer) water will get into the drywall. It might after 4 coats too... So I want that water to be able to escape, not be trapped in a vapor barrier.
Best Answer
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)