To me the bass sounds like a very clean Ric with flatwounds played with a pick. I would approach it from the perspective of trying to set the attack and release on a compressor correctly. I think you want a medium length attack to let the pick attack come through then let the compressor clamp down. So, that means a slower release. I'm not home so I can't give you any specific numbers but the key is compression. Wild guess maybe an attack around 100ms and 200-250ms release with a high ratio...maybe 4:1.
Good luck.
