My answer would echo MRL's. My one year old rescue did this when I got her. I have ZERO tolerance for barking in the car, and I made this clear from day one. It isn't just a question of it being embarassing, it is a question of safety (could startle people, kids on bicycles, people on horseback), and is disrespectful to me as a driver to have a dog barking in my ears.
I did pretty much what MRL did. ONE bark and I would go ballistic! She got the message. If I had to pull over and turn around to give Keeta the full effect of my expectations for her to quiet, I did. I trained the "quiet" command from day one. It took a long time for a dog with no previous training to understand what a command was to start with, but I kept at it and she got it. I made sure to praise and reward her "quiet". If I saw something that I knew would set her off, I would tell her quiet even before she started barking, and praise the heck out of her when she did stay quiet.
She will stay quiet when left in the car in a parking lot, for example. Because she knows that is what is expected of her, even if a small frou-frou dog is in the next car barking its head off at her, she will ignore it. It is all training. Take the time and take the effort, and the results will be well worth it!