There is a lot of confusion about the terms active and passive when it comes to pickups and electronics. Here's the deal:
A passive instrument doesn't need a battery. It has passive pickups and passive controls. All of the power that the instrument produces comes from the current generated in the pickup coils. The controls only reduce the power from the pickups, and the pickups are affected by electronics outside the instrument.
An active instrument has a battery to provide extra power to the output. An active instrument may have active pickups or passive pickups.
An active pickup has a power connection from the battery to power a pre-amp built into the pickup itself.
An active instrument with passive pickups has a pre-amp in the control cavity. This pre-amp may be a simple buffer that only stabilizes the output voltage so that the pickups are not affected by electronics outside the instrument. Or the pre-amp may be more complex and provide increased gain along with boost and cut of various frequency bands for on-board equalization.
Instrument manufacturers and retailers are often unclear about this distinction when they advertise an instrument. They may say that the instrument has active pickups when in fact it has passive pickups with an on-board pre-amp. Alternately, they may say that it has active electronics when in fact it has active pickups and passive electronics designed to work with the active pickups.
Most Bartolini pickups are passive for 2 reasons. This approach offers flexibility in that the pickups can be used in a passive instrument or in an active instrument with an on-board pre-amp. Also, it requires that the pickup coils have a voice of their own. This is in contrast to active pickups that are often made with coils that have a very flat response and have a voice created by the internal pre-amp.
Musicians often develop preferences for active or passive instruments based on this misunderstanding as well. It may be that they think they prefer passive instruments because they have had an instrument with active pickups and they prefer the coil voicing of the passive instrument. They may not realize that the same coil voicing can be achieved in an active instrument that simply has a buffer at the output. Similarly, those prefer active instruments may think they need active pickups to get the control, stability, and predictability that active instruments provide when in fact they just need to add a pre-amp to their existing passive instrument.