Actually, if the wallpaper is on there real good (not loose anywhere), you can SKIP removing it IF you paint/seal it with KILZ original OIL base primer! You MUST use exactly this product (NOT water-based KILZ latex primer) or any other. This oil-based stuff will NOT wet/soften the underlying 'glue', and will dry almost instantly (leaving no time for underlying glue to soften) - just be sure to apply with roller and do NOT 'overwork' the roller on the surface. The final product (when dried) will act as a sealer, and prevent any water from texture or topcoat(latex) from penetrating underneath the kilz to soften glue. The wallpaper/glue will become just like another paper layer on gypsum wallboard!, sealed in safely with the KILZ.
I have had FABULOUS results doing exactly the above - the wallpapered/kiltz'd surface is so perfectly smooth that I was able to only very lightly texture it simply using a roller with semi-watered down joint compound, then top-coat with latex. Let joint-compound dry 2 days.
Also, if you do have just a few spots where paper is loose, use a razor blade to first remove JUST the loose paper, then apply kilz over everything and let dry before patching/touching up any areas were paper removed/uneven and let that dry before applying overall texture. For a bathroom, I'd probably apply another layer of kilz OVER the texture, just to help seal it in.
One area we did pull the wallpaper off left such an un-even surface, it didnt turn out any were as nice as the ones sealed with kilz, making me wish I knew the KILZ trick from the beginning! Again, one final warning, use ONLY the KILZ ORIGINAL oil-based primer (white&red can) - it is specially formulated for near-instant (1 hour) drying, and using anything else could end in disaster. Also, the fumes on this KILZ necessitates adequate ventilation - but it dries in 1 hour and fumes are gone just as fast IF you ventilate well.