Now we're talking! You're playing a shuffle on bass, which fits the natural feel of the song. Feels better, doesn't it?
You're still rushing. Listing to the part that starts about 0:34. Feel how the bass shifts ahead of the beat and messes up your groove? Zoom in on the wave form and you'll see it. It never quite settles down after that, even into the change up. When you go back into the first part around 1:40, you're consistently pushing the beat.
It's it a tough habit to break, but now that you're aware of it you can work at it. What seemed to help me was listening more to the drums. Focus less on what you're playing, and more on what you're hearing. Think of the bass as a kind of extension of the drum kit, and just let your fingers find a place in that groove. (I know you're playing with a pick. Man, you should try finger style. It's massively more fun to feel connected to your bass through the fingertips rather than a piece of plastic!)
Are you monitoring the guitars while you lay down the bass track? If so, don't. Just the bass and drums. It's easier to track bass if you don't have any possible timing mistakes on the guitars messing you up.
Here's another idea if you're trying to get your bass locked in with the drums. On a lot of blues shuffles the drummer will lay back behind the beat on the snare backbeat. It gives the song a kind of swaggering, laid back feel. I try to listen to that snare and cop its timing. That will get you playing behind the beat instead of rushing. Something that's fun is to do an eighth note shuffle on 1 and 3 while the snare lays back on 2 and 4. Like: ba-bom (whack) ba-bom (whack). It's easy to lock in because it's a kind of call-and-response thing, between the bass and snare.