Not Bluetooth, but tempting to give this idea a try using a sub-$1 microcontroller [0] implementing a software-defined radio with a PCB trace antenna which is powered from the kinetic energy when you actually hit the key.
Not bluetooth, but every key being wireless is great for ergonomic keyboards. You can tune the layout iteratively without soldering anything. I think there's enough kinetic energy for a short transmit each time the key is pressed, but currently the energy is now dispersed to bounce the key back up. A thick keyboard (like kinesis or dactyl) does have space for a CR1616 battery under each switch though.. That with an NFC/RFID chip for each key might actually enable a truly wireless keyboard.