A quick google search pulls up a couple of tutorials on how to tether your smartphone to your laptop, or even several laptops to share internet, but none of these solutions would let you run the setup headless.
Judging by the thread here RPi Bluetooth is fiddly at best and at worse a firmware nightmare, requiring a fair bit of tinkering and access to set up. Though once setup -- provided the bluetooth stack doesn't crash -- it should recover the connection gracefully enough the next time the client is in range. Thought that doesn't help with the first time a particular phone gets in the car.
Maybe I'm not being fair to the little board that can, Bluetooth by its nature is fiddly, it might not be a RPi problem at all. Low power signals are easily interfered with after all. All of the big automotive companies have spent large sums of money for systems that work consistently with their customer's phones.
This site might provide some tools to help you. Sadly, since Bluetooth is an actively licensed brand, open source solutions may not be be feature rich.
Finally -- and I hesitate to offer this -- a Bluetooth Beacon may not sound like what your after, but there is a solution direct from Bluetooth.org that supports the project on a RPi, so it might be worth a look. It will require signing up for their developer's kit and not having done that myself I can not speak for their treatment of hobbyists though the fact that they have development kits for RPi and Arduino 101's is promising.
Since Bluetooth beacons are being developed to provide location aware advertising (sic) to smart phones, then this branch of the technology is likely to be better supported in the future and might suit your needs with a little creative coding.
If you have the means to develop an app to run your project, you can use something like the Eddystone project to tag smartphones that get into your car. From there, its in the hands of the user.
If your unsure of what a Bluetooth beacon is, I can give a quick example. Target runs them to drive folks to their Cartwheel savings app. When I walk into a Target store (or even drive through the parking lot sometimes) I get a banner notice on my phone. Its inviting me to open their app and connect to the deals available in the store. While you are hopefully not going to be serving ads to the people getting into your car, the principle is the same.