Imagine a young Bob Dylan and an equally young Mavis Staples—married. It could have happened, according to Mavis. She recently told the story via telephone from her Chicago condo that faces cold Lake Michigan.

“He told Daddy, ‘Pops, some day I’m going to marry that Mavis girl.’ And Pops said, ‘What are you telling me for? Go tell Mavis.’

At the time, Dylan hadn’t yet gone electric, and the Staples Singers were years away from message song hits like “I’ll Take You There,” “Respect Yourse...