So I've come up with some other possible features to add which would be incredibly nice to have:

Automatic triggering of the transmitter

This could be done by using a bike wheel sensor, of the type commonly used with $5 bike speedometers.

Determining and transmitting actual location

GPS could be used here, but I want this device to be as cheap as possible. I live in a city with a free WiFi network and an overabundance of wireless access points, so my current idea is to use an ESP8266 to sniff for nearby APs, and then do one of two things - connect to a free WiFi network, send the list of APs to the Google Geolocation API, and then send the location to a preconfigured email address; or simply send the list of seen APs via radio to the person tracking the stolen bike. Since the ESP8266 is quite power-hungry, it will only determine location when sent a message over radio.