There are several ways depending on your situation. 1. place insulation in the walls (foam insulation can be applied when drywall is already up). 2. use double sheets of drywall or a better option is to use sound board in place of drywall. 3. make sure all openings into bathroom are filled or tight with material. 4. use as much sound absorption material (cloth, foam, etc) as possible. Good luck.

Colorado covered it all. Although you don't want carpet, it would help in this situation. There are machine washable carpets you can cut to fit from JC Penney and on amazon.com.

Mounting a second layer of acoustic drywall (5/8" acoustic drywall = $3.29/sf = 18 dB of insulation) or you can mount normal drywall using Green Glue ($1/sf + $1/sf for drywall = 18 dB).

Not many foam insulation products carry acoustic ratings. Of course, if you can find a spray foam that has acoustic ratings that will be the least damaging.

The next thing to change = hollow core door. That cheap $60 hollow core door is letting out plenty of noise. I would start with the new door and see what noise is left. Go ahead and spend $150-$200 for a solid core door and see how you feel about the noise after that.

An acoustic retrofit is one of the most expensive "refits" that you can attempt. Start with the door (cheapest, fastest, most bang for your buck) and go from there.