Bright, 68, was hit by a private Academy Bus as he crossed the street at about 6:30 p.m. Saturday in his Manhattan neighborhood, police Detective Bernard Gifford said.
There were no arrests as of Sunday but police said the investigation was continuing. The bus driver told police he was not aware that he had hit anyone.
He played a con artist hustling Ali McGraw in 1972's "The Getaway" and acted in dozens of other films such as Sergio Leone's "Once Upon a Time in America" and "Looking for Mr. Goodbar" and in TV shows such as "Hill Street Blues."
"He always said it was the work that was the reward," said Brett Smiley, a friend and fellow actor.
Bright was arrested in 1965 on an obscenity charge for language he used in a San Francisco production of poet Michael McClure's two-person play "The Beard," which was shut down.
The American Civil Liberties Union took up the case and the charges against Bright were later dismissed in what was considered a precedent for artistic expression rights.