No, not Ingrid Bergman.
According to Batman lore, creator Bob Kane was designing the first Batman comic when writer Bill Finger brought him a photo of actor Conrad Veidt in the 1928 movie The Man Who Laughs. Said Finger: “Here’s the Joker.” And indeed, Veidt’s white face paint, receding hairline and creepy grin all made their way straight into the design for the Joker.
Comic Book Resources has a good recap of the whole story.
Conrad Veidt went on to play Major Strasser, the smooth, caviar-munching Nazi in Casablanca. (“Oh, we Germans must get used to all climates, from Russia to the Sahara.”) Strasser is the guy who gets shot by Humphrey Bogart at the airport, prompting Claude Raines’s famous line, “Round up the usual suspects.”
In what is nearly a Heath Ledger coincidence, Veidt died in 1943, just months after filming Casablanca and before ever seeing the film — just as Ledger died in 2007, after filming his Oscar-winning performance as The Joker in The Dark Knight but before the film was released.