Hi,
Although I know I am "allowed" to just install the 3 piece tub/shower insert right onto the studs, I am thinking that it might be a good idea to have some type of sound dampening behind the insert (opposite side of the wall is a bedroom)... any thoughts on if I should do this or not? If I should, what is the best (and cost effective) method to dampen the sound? If it is with fiberglass insulation, do I also add a vapor barrier? Then do I also add cement board or greenboard? Or can I just leave uncovered fiberglass insulation? Or vapor barriered insulation?
Thoughts?
Thanks,

Are all three sides of this enclosure on interior wall, any outside walls? Your best installation would be sparyed in foam but is costly, especially for a small area. Most common is fiberglass batts or rolls. Greenboard not necessary but for the extra $4 a sheet it can't hurt, drywall would be fine. Cemnet board is just a waste of time and money since this area should never get wet. Did you know they now make a sound deadening drywall too?

Yes, all walls are interior. As silly as it sounds, I would prefer to not lose the half inch thickness of greenboard/drywall. If I do use batt insulation, should I put vapor barrier or leave it uncovered before installing the shower up against the studs?
Thanks for your input!

A vapor barrier is not needed to sound proof the shower. But for only a few $$ it can't hurt. Tack up 15 lbs felt or 6 mil visqueen and you will never worry about a leak getting the insulation wet and moldy