Warner Brothers/Seven Arts
Jack, meet Warren. Warren, meet Jack. Now: you two guys go fight to the death about the future of American cinema.
But we're getting ahead of ourselves.
Starting at the beginning: the company that bankrolled and distributed Bonnie and Clyde was Warner Brothers-Seven Arts. Yes, the Warner Brothers; one of the great old brands of U.S. movie making. The company that brought you The Maltese Falcon, Yankee Doodle Dandy, Casablanca, Bugs Bunny cartoons, and countless other entertainments since the early days of the 20th Century.
At the time, the key production executive at Warner was Jack Warner himself. And for about fifty years, he'd run the studio's production unit with an iron hand. In the process, he helped to make major stars out of actors such as Bette Davis, Humphrey Bogart, and James Cagney. He was truly one of the movie business's great old warhorses—an industry giant.
But, by 1967, Warner was also part of an era that was fast fading away, and it was hard for him to understand—let alone appreciate—all the radical changes that were occurring in the film industry during the 1960's.
While Warner Brothers bankrolled and distributed Bonnie and Clyde, the film's actual prime mover and producer was its star, an up-and-coming actor named Warren Beatty. Beatty was known at the time for being matinee idol-handsome, and many people assumed that his stardom had to do more with his looks than his intelligence or talent. So he had some serious things to prove.
He also had as big an ego as Jack Warner did, and the two had a super uneasy working relationship. There's one story of Warner pointing to the studio's water tower with the familiar initials "WB" on it, and asking Beatty whose studio this was. Beatty responded that this might be Warner's studio but the initials—"WB"—were his, Warren Beatty's. (Source)
But the main problem between the two was "a generational thing." Warner was part of a fading Hollywood era, and Beatty was a young buck out to do things in a new and very different way.
It's interesting, too, that just as Bonnie and Clyde has been called "the first modern American film," the film was also an example of the changing of the guard in Hollywood. Shortly afterwards, Warner would retire. (Source)
And the film would launch Beatty on his long and successful career as an actor, producer, writer, and (sometimes) director.