He was a songwriter for Stax Records, and split his time between there and Detroit, where he moved from Mississippi as a teen. He wrote "Respect Yourself" with late R&B singer-songwriter Luther Ingram for the Staple Singers; it became Stax's biggest hit.
He was a member of the Detroit group the Falcons in the late '50s and early '60s, alongside longtime friend and future solo artist Wilson Pickett, whose recording of Rice's song "Mustang Sally" was a big hit.
Survived by his wife Laura, three sons, Rodney, Dwayne, Bonny, Jr., two sisters, Mary and Berta.