Although there are some hi-tech materials in use, the very large majority of bass guitars are made of wood. The critical consideration here is the hardness or softness. It's actually quite common to see a combination of different woods employed in a single instrument to create a balanced overall timbre. Hard woods such as maple, rosewood and ebony give a bright tone with plenty of attack, whereas softer woods such as alder, swamp ash and the coincidentally named basswood, give a more subtle and darker sound.
Most woods have imperfections somewhere in the grain that can produce 'dead spots' - notes with less sustain or resonance - so some companies such as Status and Modulus use synthetic graphite in the construction of their instruments. This gives the bass enhanced sustain, and an even sound across its range.
Wenige (Millettia Laurentii)