?!??!
First, you think this is on any bass at all, and you don't tell us which kind of bass or gear, or strings you have. If you have a sustain weak bass from the start on there's nothing added pickups can do. Say if you have a beatle Hofner bass, or semi hollow bass. No pickup will be able to increase sustain on any bass, just electronics will do. Acive pickups like EMG has this "limiting" or compression built in, due to their batteries but it is moreso increased output than anything else. Passive pickups which has huge pole pieces like Seyomur Duncan Quarterpounders will mimick a natural compression effect only, but not really sustain.
The only way is to buy another bass, which is more dense and heavily built, and has hardware, such as a rigid stainless steel bridges and frets, nut, neck and so on. The only thing that will increase sustain temporarily on any bass, is to step up a gauge or two on your strings gauge, and it works mainly only when the strings are brand new.
When doing any passive pickup witch lots of winding, you're only increasing magnetic string pull, and it will hamper the strings sustain. If you're backing them off, screwing them down towards the body, you'll lose significant output. Also, as said, lots of winding will not make it sustain any longer than before.
Sustain should be measured on the bass, like if the bass did not have any pickups at all on it. You should rest your ear against the body and listen instead.
From there you can only work with output. While compression/limiting may seem like the sustain increases it's not. If you play industrial, you may use drop tuning, and lo and behold, using drop tuning on the lowest strings on a regular scaled guitar kills sustain on the lowest strings. You'll definitely need a multiscale, or fanned frets bass. Don't believe me? Take out ANY Ltd, Ibanez, Brice, Dingwall, that has fanned fret and compare - say - low B sustain to ANY regular scaled basses low B.
Those rings longer! Period!
Just another way - of many others - to produce long sustain at low notes. If the low string are too short scale, it will die out quicker. OTOH, bassists aren't too excited about as long sustain as possible at all times. While I do think it has some merit, i e that you can damp and shorten the decay of any note on a long sustaining bass, it's harder to get it the other way around, like increasing the sustain of the strings, on a very sustain-weak bass. Then you'll have to resort to electronics, pedals, on board preamps/limiters and the like. Pickups will do nothing. A pickup at the neck position (like an EB0 bass) will sound like it has more sustain but it hasn't. It picks up the sound and oscillation closer to the middle of the string where it oscillates the most so to speak, and at widest amplitude, so the pick up picks it up a bit easier, but still, nothing can increase the bass natural sustain, only make it louder or softer through amplifying or electronics.
If you don't believe me, watch here, the ending low note B, on a Dingwall, fanned fret bass, 37 seconds, without compressor:
