I might as well post this in the Jazz thread, but this piece "Salt Road" by Enzo Favata and inspired by Ethopian folk music, has a really seductive bass line:
In this piece "Nikriz", Hassan Erraji fits Turkish tradition music into the 4/4 rhythm and repetitive phrasings of western pop music. This is a sure recipe for kitsch, but the bass line is still delectable.
If you're into metal, Overkill I find has some of the best bass work that doesn't get lost in the mix. D.D. Verni is a beast and one of my inspirations
Wow, sounds like Korn if the bass wasn't just midrange-deprived clicky noises.
As for bass-driven music, anything involving Dominic "Forest" LaPointe counts, I guess.
Especially his work in the power trio Teramobil:
And I guess Spasm counts since they don't have any guitars, only bass.
Your definition of 'music' might vary to mine, but if your mind is open to some really grimy experimental metal, I'd recommend Palehorse. They split some years ago and were only ever really known among the British underground, but I always thought they were tragically underrated. Two basses, no guitars, very nasty!