Born near Short, Mississippi, Busby attended the common schools of his native city, Oakland College, Yale, Mississippi, and Iuka Normal College at Iuka, Mississippi, taught in the public schools of Tishomingo, Alcorn, and Chickasaw Counties, Mississippi from 1903 to 1908. He was graduated from the George Robertson Christian College, Henderson, Tennessee, in 1905 and from the law department of the University of Mississippi at Oxford in 1909. He was admitted to the bar in 1909 and commenced practice of law at Houston, Mississippi. He served as prosecuting attorney of Chickasaw County 1912-1920.
Busby was elected as a Democrat to the Sixty-eighth and to the five succeeding Congresses (March 4, 1923-January 3, 1935). He was an unsuccessful candidate for renomination in 1934. He resumed the practice of law in Houston, Mississippi, until his death there on October 18, 1964. He was interred in Houston Cemetery.