To wideyes : Last week, I have put a new Bartolini 8S with new 500k cts pots and new .022mfd mallory cap on a Fender mim squier series p-bass. I have used the Bartolini wiring schematics provided with the pup. New jack input socket and wire too.
Previously, I have used the Fender standard p-bass schematics with new standard pots and new cap (250k cts pots and .047 sprague orange drop). Using the Fender standard p-bass wiring and the standard pots and cap, the sound was dead, I mean it sounded like a huge amount of bass and few low-mids frequencies, but nearly no high-mids or high frequencies. Very dark sound, not very musical.
So I swapped the 250k pots for 500k pots, wired everything following the Bartolini wiring that was in the pup box, with the .022 mallory cap. And it all worked perfectly well ! So, this is probably the best combination for the 8S when put on a p-bass.
Maybe a combination of 250k/500k pots would be a good idea too, but I lack the elementary ary skills and little time to experiment by now.
Hope my message is clear and will help, I'm not an english speaking person.
ps : at last, I found the best for this bass and the bartolini 8S is vol250k/tone500k with .022 cap.