His hits include Do You Still Drink Margaritas; Playboy; Let’s Start a Rumor Today and the classic song penned by Merle Haggard My Past Is Present.
Durham first performed professionally at age 11, appearing on Billy Mize's TV show.
He performed solo and occasionally with his brother Wayne on local shows such as Town Hall Party, Trading Post, and Cliffie Stone's Hometown Jamboree and in 1953 he joined Cousin Ebb's Squirrel Shooters, which was the house band for the Pumpkin Center Barn Dance.
In the 1960s Durham signed to Capitol Records and released several singles, including his take on the Merle Haggard song "My Past Is Present".
Later Bobby joined The Crickets, onetime backing band for Buddy Holly; He would spend the next five years touring with them.