Mass is only one tool for bass attenuation. It normally requires a system approach incorporating sound isolation, breaks, absorption and/or blocking. Adding too much mass can mean poor sound quality. It means the bass will hang around in the room, degrading articulation, dynamics, timbre, etc...
This does sound like a difficult room. It's hard to answer your question without knowing your goals, budget, equipment, etc. The room can be optimized to your particular constrains, but will that be enough to satisfy your expectations? Is there another room to consider?
You are way ahead of most people by considering acoustics! Without knowing the scope of the project, I'll agree that you can most likely address the sound quality issues (room modes, 1st reflections and reverberation times) later, but now is when you want to look into potential noise control...