I have a bathroom that has been painted with sand for texture. Will sanding remove it effectively? If so, what kind of sandpaper or screen should I use?

When redoing a bathroom for a client with the same problem we realized it would be much faaster to cover the existing walls with 1/4" sheetrock dry wall and then paint the new wall. This sanding the paint off with take a very long time. Also you may have to replaster some places in the wall after sanding.

A power sander with 100 grit should remove the texture if its not on to heavy. Once off a light coat of spackel where needed and good coat of prime paint should do the trick.

If the texture was indeed applied with paint, and not part of the original surface, then the gentle use of a paint scraper or sanding block may take it off.

If however that doesn't do it, you could skim coat it with joint compound. Here's a place that tells you how that is done.
http://www.plaster-wall-ceiling-solutions.com/skim-coat.html

I still say the fastest way to get rid of the texture on the BR wall is to put 1/4 drywall over it. Whaen you sand these walls in an effort to remove the texture holes and pits will be amde by the sander. then you ahve to fill and patch and prime them before painting. Just cover them up, tape the seams, prime and paint. Much simplies believe me after about 25 years experience I know.Also this adds warmth and "quietness" to your bath room.

I must disagree with you Squeekysmom. You can rent large drywall sanders that connect to a vacuum to remove the texture. Once you cover the walls with new drywall you need to fix the edges where it meets the door, window, and floor trim and perhaps the ceiling. Dont forget about extending the outlets and switches out as well. The power disk sanders they rent work real well and do not take that much time to do.
Either way you may need to spackle a bit, but its more professional to do it without adding layrs to the walls.

if I was you, I would go for drywall