I am a nervous reck
having Cookie loose in the car while I am driving so I make sure she is in her car seat/bag while I am driving.
If there is someone else in the car w/ me than its ok for her to be loose but I don't let her walk or roam around the car.
Biddy's Mom - if Biddy has a favorite bag/purse he may associate it w/ being a safe place so try placing him inside the bag and bringing him into the car while in his bag. Putting a favorite blanket or toy inside would help too. Hope this works for you and Biddy.
My Cookie just loves her bag b/c she knows she will be going out w/ mommy and I only have to go about a block before she is getting comfortable to take a nap...