Insulation, Radiant and Vapor Barriers - insulate attic over bathroom

I have an older 1952 house with the only insulation is the actual attic. The insulation is obviously very old. In my bathroom I have been having a big problem with water developing during a shower on the ceiling. I was advised that this was caused by the fact that my ceiling is obviously very cold. I am figuring since it is so old I should add some insulation. I was wondering if anyone has recommendations on what I should buy to put over the bathroom. I dont want to do the whole attic yet for financial reasons. Also my master bedroom which is in the corner of the house gets so cold. The walls are not insulated other than the insulation board they put on when they resided the house. I caulked all the windows but it is still bad. My question is, if I add insulation in the attic over the bedroom will that help? Also any advise on making it warmer without having to rip the walls down?

R-30 paper-faced fiberglass batt. Install face down (paper up against the bathroom ceiling).

For walls, you can blow insulation in by cutting a hole up top and pumping some cellulose in there.

When I buy the r30 can I lay it over the existing insulation with the face side down or do I have to remove it? The current insulation has the the paper back facing the sheet rock.

Rip out the old suff if it's no good. Be carefull not to create a double vapor barrier anywhere, as this is a moisture trap. Yes, paper side down in the attic or always to the conditioned space as a rule on thumb.