Bucknum participated in 11 Formula One World Championship Grands Prix, debuting on August 2, 1964.

After Formula One, Bucknum drove in the USAC Championship Car series, racing in the 1967–1970 seasons with 23 starts, including the Indianapolis 500 in 1968–1970.

He finished in the top ten 10 times, with his one victory coming at Michigan International Speedway in 1968.

He was the father of Jeff Bucknum, an Indy Racing League and American Le Mans Series driver.

Ronnie Bucknum died in San Luis Obispo, California following complications from diabetes.