Are you talking about some kind of Bluetooth device with an inbuilt lithium battery? If you are going to build it into the radio, you will not want a battery power Bluetooth device. You do not want to have to pull out your radio every 2 years to change the lithium battery, especially as it will be powered by the car battery anyway.
I am not sure how well you can integrate a bluetooth device into a radio anyway. You need to be able to ask the bluetooth device to make itself discoverable so you can pair to it. You definitely do not want to have it permanently discoverable.
I assume you have given up on the FM transmitters as a way of getting music into your car radio, and so now you want to find a bluetooth device that you can connect directly to the radio's audio circuit. It may be possible, but you can get great bluetooth radios with handsfree phone support for about $150. Is it worth trying to make a non-integrated bluetooth device work?
It would be much easier adding an audio input lead that you can plug into a standard earphone socket.
Richard