He was a member of the New Mexico Territorial senate, 1899–1900; chairman of the Territorial central committee in 1905 and 1911; member of the State constitutional convention in 1910; and a member of the
Republican National Committee, 1920-1924. Bursum was appointed on March 11, 1921, and subsequently elected on September 20, 1921, as a
Republican to the United States Senate to fill the vacancy caused by the resignation of
Albert B. Fall and served from March 11, 1921, to March 3, 1925. He was an unsuccessful candidate for reelection in 1924. He served as chairman, Committee on Pensions (Sixty-seventh and Sixty-eighth Congresses). Subsequently, Holm Bursum pursued a newspaper career in
Washington, D.C. and in New Mexico until his death in 1953. ==Later years==