Practice playing.
Every type of bass has been used for all those styles of music. The difference is the fellow or lady playing the thing. You can play all of that music on pretty much any reasonable quality bass. By reasonable bass, I mean something you can plug into a DI and it sounds good without any polishing on a desk, no amp, no effects, no EQ tweaks. Everything else is fluff. It's fun but it's still fluff. A decent player and any decent bass and you're good to go.