This bass uses a cheap piezo disk from an electronics buzzer (the 'radio shack' pickup- follow the links for details on the electrical side of things) that cost me ZAR5.00 (about $0.70). The pickup is connected straight to an output jack with no tone or volume controls.
This type of pickup gives a surprisingly good sound but does need a bit of modification to work properly. The pickup needs some soft material around it to cut down on high-frequency sounds (like squeaking string noise) and to make the sound from the strings louder than sounds from the body (like tapping on the neck with your hand).
On this bass, I filed a channel in the bottom of the bridge, and placed the pickup between two layers of felt inside the channel. Underneath the bridge, I placed a layer of cork (about 0.5mm - 1/32 inch).
Narrowing the contact area of the bridge to the body helps isolate the strings from the body a little, and the cork and felt help to isolate the pickup from the body. After making these changes the bass is much easier to play without extra noise.
Pickup placement from side to side is also critical- you will have to move the pickup around a couple of times and play the bass while listening carefully to balance the sound between the two strings.