There are several ways to do this and the level of success varies, based on how well they actually prevent the energy transfer to the backside of the "enclosure". Total isolation and de-coupling are best, but most difficult but if you can't do both, isolation is the best single method as long as you can remove some of the drywall/plaster to install a box that is attached to the studs with a flexible adhesive (like polyurethane or silicone) and not touching the wall on the other side. Once it has set, the drywall can be installed by screwing it to the studs and the face of the box. It's not totally isolated, but by using the flexible adhesive, it's better than being screwed to the studs. A soft enclosure can work, to a point, but since bass is the problem, it's best to use something rigid and build the box with a baffle (face). Make sure to use sealant to attach the drywall to the box- if you don't include a baffle and leave sealing the edges to the drywaller, there's no guarantee they will and that means something will vibrate because of air leakage.
Unless you're prepared to go through this and possibly more, you won't stop all of the sound going to the bedroom- you would need to be isolated and de-coupled for that to happen and most of the low frequency energy reaches other areas though the structure.