Household Hints & Help

Don't do it.

Removing old wallpaper is not easy but worth the time and effort.
You will regret painting over wallpaper, the seams will show and perhaps the moisture in the bathroom will get behind the paint and cause the whole thing to blister.

Get an old spray bottle, spray the walls with a combination of hot water and vinegar.
Before spraying, gently score the walls so that the sprayed solution will get behind the paper.
Scrape off after several sprayings. Be patient. The solution will take some time to soak in.

Use a razor blade(gently) or wallpaper scraper to do the job. Even an old putty knife might work.
Smooth out the dry plaster by sanding, then prime and paint.

If it is wallpaper over sheetrock, the job is tough. I'd remove what I could, knowing that I would damage the paper covering the sheetrock. Allow to dry and plaster over with joint compound, then sand, prime, paint.
Good luck.