I don't claim to be an acoustic engineer, but I have some experience in building walls in apartment buildings to (attempt) to contain sounds. There are two issues. One is sound transmission through the structure, and the other is sound transmission through air. You will want to address both for bass playing. If you build a wall that creates an air gap between the existing wall and the new wall surface, it is the start. You will want to use light gauge steel studs or really crappy wood studs. It's not a structural partition. A couple layers of GWB on the sound side of the wall, with acoustic sealant in both layers is good. Use adhesive instead of screws to attach the second layer of GYB. Fill the stud cavities with dense mineral wool if you can manage to pay for it. Unless you are on the ground floor or in the basement, you will have to think about the floor as well. Putting your amp on a piece of playground matting helps a whole lot. Don't forget the ceiling. Sound can get into the ceiling cavities and travel a long way. If the building is concrete, then you will have to make sure there's no structure borne sound traveling all around the building. You would do something similar with channels and more GWB and mineral wool. Think of it as building a really dead box around the room. There are other products that I'm a whole lot less familiar with that are rubber or something similar. I assume they work, but there's no substitute for an air gap behind a sealed surface that keeps the sound mostly in.
If you angle the walls just slightly to avoid parallel hard surfaces, it will make it more pleasant for you. As long as you are doing all this work, get them out of parallel by a couple inches. I know how expensive square footage is in NYC, so this is a pretty big thing. But so is adding a second wall. I have made big mineral wool panels for the basement music room, and they work well to keep the sound from getting harsh in the room. I'm less sure they keep the sound in the room. For what its worth, the music room is built with wood studs, only a single layer of GWB, and fiberglass insulation. It's set into a concrete basement structure, on a thin concrete rat slab with just dirt below. It may even be hollow in spots. The neighbors don't complain, but then the kid next door on one side is a drummer and the couple on the other side used to play in a band that rehearsed in their basement.
Easy for me to say, since I'm busy spending all your money.