Sound Proofing the wall between bathroom and bedroom
You deal with it by doing couple of things in parallel:

Decouple sound sources, quiet pipes in the walls


Make sure to wrap all pipes in either soundproofing mats or just carpet underpad (that's what I did), especially where the pipes touch the framing, to reduce sound transmission directly from the pipe.
Make sure nothing rattles/moves, e.g. all pipes are securely attached.


Add more mass to the wall, reduce the sound from the bathroom itself


Use thicker drywall, or double drywall, with Green Glue between the layers. 
Add Roxul Safe'n'Sound or similar soundproofing bats into wall cavities. This will also somewhat help with noisy pipes.
Use acoustical sealant in all outlets or other openings in the wall.


Deal with the noisy fixtures


Get a quieter bathroom fan, if yours can be heard outside of the bathroom.
Make sure your water pressure is not too high, install/replace water pressure regulator if needed.
Invest in quality plumbing fixtures. I found that cheapest faucets often make much more noise than quality ones. Same for shower head. Also, 2 gpm showerhead will typically be quieter than 2.5gpm (less water). 


In any case, if someone takes a shower, it will still be heard in the room right behind that drywall. Doing all this will reduce the noise, but not eliminate it completely. I did succeed to make my basement much quieter doing basically what I wrote above, and it wasn't terribly expensive (I didn't do double drywall though), just don't expect miracles.