Born in Springfield, Massachusetts, Bowles attended Choate Rosemary Hall in Wallingford, Connecticut, graduating in 1919, and the Sheffield Scientific School at Yale University, earning a Bachelor of Science degree in 1924. After working for a year as a reporter, Bowles became an advertising copywriter and later established the Benton and Bowles advertising agency with William Benton in 1929. Despite the Great Depression, by the mid-1930s Benton and Bowles was a multi-million dollar company. Bowles served as chairman of the board for the company from 1936, and by 1941 was making $250,000 per year.

Bowles sold his shares in the company in December 1941 for a substantial profit and attempted to join the Navy, but was rejected because of an ear problem. He then took a job with the state of Connecticut in the wartime rationing administration, later becoming state director of price administration. He was appointed by President Roosevelt in 1943 as administrator of the Office of Price Administration, and also served on the federal boards for War Production and Petroleum.

In 1946 he was appointed director of the Office of Economic Stabilization, and also ran an unsuccessful race for the Democratic gubernatorial nomination in Connecticut. That year Bowles also was one of the American delegates to the first UNESCO conference in Paris. He served as special assistant to UN Secretary General Trygve Lie in 1947-8, and was International Chairman of the United Nations Children's Appeal from 1948-51.

Bowles was elected to the governorship of Connecticut in 1948, defeating James C. Shannon, and served one term, during which time he signed into law an end to segregation in the state national guard. During his term, Bowles was also active in improving education, mental health, housing and workmen's compensation. His liberal views and policies while governor are attributed by most as the main reason he lost his re-election bid in 1950.

He was appointed as U.S. Ambassador to India and Nepal by President Truman, serving from 1951-53. He then won a seat in the House of Representatives for Connecticut's second district, serving one term (1959-60). On more than one occasion he was an unsuccessful candidate for the Democratic nomination for the U.S. Senate.

Selected as a foreign policy adviser in 1960 to Senator John F. Kennedy, Bowles went on to act as chairman of the platform committee for the Democratic National Convention that year. President Kennedy appointed Bowles to the post of Undersecretary of State in 1961. In early December 1961 he was replaced by George Ball as Undersecretary, a consequence of his perceived failure to adequately fulfil his duties as an administrator in the Department of State, and his earlier leaking of his opposition to the Bay of Pigs Invasion. His removal was made part of a broader bureaucratic reshuffle, which became known as the 'Thanksgiving Day Massacre.' In December 1961 he was named the President's Special Representative and Adviser on African, Asian, and Latin American Affairs, and Ambassador at Large. Ostensibly the new position was a promotion, but as was recognised by all involved at the time, this improvised posting was intended to ease Bowles's removal from the Undersecretary's office. In July 1963 Bowles's was again made Ambassador to India, a position he would hold through the remainder of the Kennedy administration, and for the duration of Lyndon B. Johnson's presidency.

In March 1967, Bowles was formally petitioned for political asylum by Svetlana Alliluyeva, a writer and the only daughter of Joseph Stalin, which was then provided and arranged for her to leave India immediately for Switzerland, via Rome.

Bowles died at the age of 85 after suffering a stroke in Essex, Connecticut and is buried there in River View Cemetery.