Does it have a LED blinking when incoming calls? If yes, you could always connect it to a regular bjt transistor that works like a simple switch.
Question is if that is practical. Whenever somebody rings, you might have to disable bluetooth so you can use the phone (not handsfree) when talking. The nature of your phone will decide that.
Also, I have dismantled an old sony ericsson bluetooth handsfree, but I faced a major problem. I couldn't take it apart without destroing it. That is - you have to cut the plastic encapsulation very carefully, and un small pieces at time. If you do that too fast you run a high risk at destroy the pcb inside.
The applications that people come up with is so... innovative!
Anyhow... If a phone call is coming in, I asssume, the bluetooth handfree speaker will ring?
If this is correct, I would advise that you remove the speaker and link the wires to a 555 timer (monostable) and use the output of the 555 to drive your BJT or MOSFET that will drive the motor.
SO in summery SPEAKER -> 555 -> BJT/MOSFET -> MOTOR
Remember that in the above intance a new power supply is needed because I dont think a handsfree bluetooth will supply adaquate power.
you can also use DTMF ( bit complicated) you can controll the direction of the car using this. CM 8870 is a dtmf decoder. you can diss assemble the blue tooth recever, take out the audio out, link it with the DTMF decoder and take the out puts from the data output of cm 8870, then use L293D for the motor drving.
press 2 for fwrd,
8 for back,
6 for right,
4 for left.