While a student he engaged in agricultural work, retail sales, and as a substitute rural mail carrier.

He was admitted to the bar in January 1928 and engaged in the practice of law in Greenville, South Carolina.

Ashmore was elected as a Democrat to the Eighty-third Congress to fill the vacancy caused by the death of Joseph R. Bryson.

He was reelected to the Eighty-fourth and to the six succeeding Congresses (June 2, 1953 – January 3, 1969), during which time he was a signatory to the 1956 Southern Manifesto[1] that opposed the desegregation of public schools ordered by the Supreme Court in Brown v. Board of Education.

He was interred in White Oak Baptist Church Cemetery, Greenville, South Carolina.