Lets assume the fender bass is a precision(hopefully)...Leo intended it to sound like an upright so we're halfway there.
You need to use flatwound strings.Fenders, the GHS black tapewounds are GREAT.
Now, did this (hopefully) P-bass have the little thumbrest up towards the neck above the strings? NO?everybody takes them off cause they get in the way of rock-n-roll.Fender doesnt even put them on unless its a Vintage Model.
This where you want to pluck the strings.Right up by the last couple of frets.This is where upright bassists play and this is where the tone will come from.
Another technique is to use a pick and damp the entire set of strings with the edge of your hand and pick across the side of the pick damping each note for length and sustain.This is done at the bridge.
As far as compression goes, this is a matter of taste.I usually use a bit going in and then the same setting on the mix to sort of help it along.This is usually @3:1 sometimes a bit more and a fast release.The playing technique is usually what makes it happen anyway.
One other thing that will help tremendously is to have a very old Fender bass with stock pickups. None of the aftermarket P/U's with their windings made for rock are gonna help you get that sound.Leo knew what the hell he was doing from the git-go and why anyone would want to change perfection is beyond me.
