Go into Settings>Bluetooth>select your vehicle, then tap on the small ℹ on the right side. From there, they may be settings for you to choose to sync your contacts to the vehicle. If that is already on and you cannot access contacts, then click on the Bluetooth for the vehicle on the phone and select Forget this Device. Then turn off Bluetooth. Do a reset on the phone, holding the sleep/wake and home buttons together until you see the Apple logo and release. The phone will reboot. Now go to the car, find the Bluetooth settings and remove the pairing of the iPhone to the car. Turn the car off. Turn the car back on, the put the vehicle's system into discovery/pairing mode. You may have to consult the vehicle owner's manual to do that. Once you have it in discovery/pairing mode, go into Settings on the iPhone and turn Bluetooth on. This will put the phone into discovery/pairing mode. The two should pair, although you may need to enter a PIN code in the phone. Again, the vehicle owner's manual should indicate this. Leave them paired for a while to give the vehicle a chance to download the contact list.
The only way this would not work is if the Bluetooth for the vehicle does not support the PBAP profile.