The master behind the wheel of the Dodge Charger was Bill Hickman, I think. He was a stunt driver of extraordinary talent whose driving skills were also used in the classics, "The French Connnection" and "The Seven Ups".
Paul George, if memory serves, was the gray haired, killer side kick who rode (literally) shotgun in the movie.
Bud Eikens and Carey Loftin did most of the tricky driving with the Mustang. Eikens is the one who also laid down the motorcycle during the chase scene (Terry K correct me if I am wrong) near NBC mountain, in the later scene of the chase.
Here's a great "Bullitt" link...