I think the key is the Bluetooth profile your stereo/car has for this function. When you go to Settings - General - Bluetooth and click on the blue arrow next to your car/stereo pairing, do you a screen like the one attached?
If so, make sure that it's set to transfer the contacts you want.
If you don't see this screen, your car/stereo might just not be compatible with the iPhone 4. I don't know of any jailbreak apps that might be able to help so hopefully someone else who might know of one can chime in.
Thanks a lot.