Notice the guy in the video is reading the part! He does a great job of giving the notes full value, and the whole thing has a pretty funky feel. Nice. I'll take his slow version over any number of fast crappy sounding versions.
There are transcription books for Jaco's solos. Note for note. Read the music along with the tune. Check out how the melody works with the chords. Try to sing the part, at least the rhythm.
That's how you do it, one phrase at a time, if your reading is slow like mine, and slowed down to where you can play it without any mistakes. Then you bump up the metronome or drum machine 10 BPM at a time until you fall apart. Then you work some more.
Try to read it at each new tempo, don't be looking at you fingers.
Are you going to do it at Jaco's clip? Maybe not for a while. But working like this will pay huge dividends.
Get a Real book and do the same for other jazz tunes you like.
FWIW I'm currently abusing Dizzy's Grooving High at a snail's pace 110 bpm. You get a lot of cool ideas from the masters, its worth it. Am I going to bust it out in public? Not any time soon, but I'm having fun with it.