Practice, practice, practice. Oh, and practice.

Other than that the only advice I can give you is slap the bottom notes. It sounds funky as hell and it's so much easier. Oh and if you're just coming off of guitar, and you're used to playing with a pick I suggest NOT playing Primus. You can try though.
You need to use finger style, what he does is an up and down stroke with most of his hand. Meaning like index middle and ring.
Guitars/ Basses:
PRS SE singlecut w/Tremolo
Epiphone Sg
Epiphone Thunderbird

Waiting in the wings:
Squier Strat mod
(soon to start)

Line 6 Spider JAM
Peavey Max 115 bass amp
He uses a modified flamenco style strum. If you've ever played spanish flamenco or classical guitar its very very similar in its execution.

Check out on Youtube for Primus "Too many Puppies-Radio Jam". The video does a pretty good demo on the style. Take it slow and practice. Its one of the few bass techniques I can honestly say after fingerstyle funk that I do well. Think of your hands as being drum brushes stroking the strings.
Quote by derekwalden_-33
Thanks everyone.

Any tips on just finger playing?

Yeah, learn to alternate your index and middle fingers. Start out by just playing eighth notes on a single fret and practice alternating at a speed you are comfortable. Do this everyday and start changing between strings as well as increasing your speed. You'll be fingerin in no time!