Designing Kitchens and Bathrooms - Insulating bathroom walls and ceiling OK?

Is putting insulation in the bathroom walls a good idea? I want to insulate the exterior wall, and possibly the interior walls as they are also bedroom walls. Do I need any kind of vapor barrier plastic wrap or something because of it being a bathroom?

And how about the ceiling? There is loose insulation up there now, but it is comming out (probably) and I would put in regular rolled insulation. Above the bathroom is a "attic bedroom", which we keep cold...

We usually insulate bathrooms anyway, not necessarily for cold/heat, but for sound transmission. Using the moisture theory, the vapor barrier, if used, should go to the other rooms on the interior walls. If there is any insulation in the attic, apply unfaced insulation over it. If you have no insulation up there, then use kraft faced and lay the paper vapor barrier down toward the bathroom.

All outside walls need insulation, and a vapor barrier as does the ceiling. Walls joining other living spaces need sound insulation, which is a bit different. Is is not a necessity, but not a bad idea.

You say the vapor barrier should be on the other room side of the insulation? So I'll have the green drywall, insulation & studs, then the V.B., then the other room's drywall? Wouldn't I want it before the insulation, to keep moisture out of the insulation?