Robert Bliss attended preparatory schools in Virginia, Minnesota, and Massachusetts and then graduated from Harvard University with a B. A. in 1900.
Bliss entered the diplomatic service upon graduation and worked first in the office of the secretary of the United States civil government in Puerto Rico. From 1901 to 1903 he was private secretary to the governor of the island. After passing the State Department qualifying examination in 1903, Bliss was assigned to Venice as United States consul. The following year he was appointed second secretary to the United States embassy in St. Petersburg, where he remained until January 1907. In 1907, Bliss had been named secretary of the legation in Brussels, and the following year he served as a delegate to the international conference that considered the revision of the arms and ammunition regulations of the General Act of Brussels of 1890. From 1909 to 1912 Bliss served in Buenos Aires as secretary of the legation. In June 1912 he attended the international conference at Paris that met to consider the relief of aliens. From 1912 to 1916 Bliss was secretary of the Paris embassy; from 1916 to 1920 he held the rank of counselor of the embassy. In 1918 he was temporarily assigned to serve as chargé d'affaires at the United States legation in The Hague. Bliss was recalled to Washington in 1920 and became chief of the Division of Western European Affairs at the Department of State. He was in charge of protocol and ceremonies during the 1921-1922 Washington Conference on Limitation of Armaments. Simultaneously he served as chairman of the diplomatic service board of examiners.
A lifelong Republican, Bliss was appointed by President Warren Harding as envoy extraordinary and minister plenipotentiary to Sweden in 1923. He served there until 1927, when he was named ambassador to Argentina by President Calvin Coolidge. Bliss's career was typical of many foreign service officers. Having paid his dues in relatively minor posts during three decades of dedicated service, he was rewarded by promotion to ambassador in his final years. Bliss retired in July 1933, perhaps in reaction to the election of the Democrat Franklin D. Roosevelt as president. After American entry into World War II, Bliss was called out of retirement. He served as a consultant to the State Department in 1942 and 1943, as a special assistant to Secretary of State Cordell Hull beginning in February 1944, and as a consultant to Secretary of State Edward Stettinius beginning in December 1944. He again retired in November 1945.
Bliss and his wife collected pre-Columbian, medieval, and Byzantine art. Many of their Byzantine pieces were acquired during extensive travels in Greece and Turkey. In his retirement years Bliss engaged in many cultural and civic pursuits. He was president of the American Federation of Arts and vice-chairman of the Smithsonian Art Commission and the board of the National Trust for Historic Preservation. He was on the Board of Overseers of Harvard University (1939 - 1945). Through his many years of collecting, Bliss had become a highly regarded authority on pre-Columbian art, and wrote The Indigenous Art of the Americas (1947). He died at Washington, D. C.
Bliss was a member of the American Foreign Service Association, the Washington Criminal Justice Association.
On April 14, 1908, Robert Bliss married Mildred Barnes, daughter of United States Congressman Demas Barnes of Ohio; they had no children.