Maplins sell a piezo transducer for 99p. They are intended to produce a beeping sound if you input a 3 volt square wave. They can also work very well as a pick up. To sound anywhere near normal they need a preamp with an impedance of at least 2 meg ohms. Circuits for these are available online. They come as a copper disk soldered with a black wire and on this is a smaller ceramic disk soldered with a red wire. This second solder joint is very fragile. To protect this joint I glue pieces of spruce (I use front offcuts but any decent wood should do) on both sides. I make a small cut out to surround the top solder joint and later fill this with epoxy or epoxy plus wood dust. When all the glue is set it can be cut to shape on a band saw or with a junior hacksaw. Solder the red wire to the core of a coaxial cable and the black wire to the shield. (best done before the glueing)

I trim the wood so it is a comfortable push fit under the bridge. (Piezo pickups always sound better when under some pressure) The pick up could be hard wired to a belt fixed preamp with standard jack socket connections to an amp or mixing desk. If you are into electronics this can be a nice weekend project.

Some guitar effect pedals have a suitably high input impedence. The effect doesn't have to be turned on. A bit of advance trial and error could be useful.