Answer by taking a quote from the following article:

Morgan Gardner Bulkeley (December 26, 1837 - November 6, 1922) was an American politician, businessman, and sports executive. A Republican, he served in the American Civil War, and became a Hartford bank president before becoming the third president of the Aetna Life Insurance Company, a post he held for 43 years. He was elected to the National Baseball Hall of Fame in recognition of his role as the first president of the National League. Bulkeley served on the Hartford City Council and was a four-term mayor of Hartford.

Bulkeley's short career as a baseball executive coincided with the beginning of his political career. From 1874 to 1876, he served on the Hartford Common Council and the Board of Aldermen. When Thomas O. Enders resigned Aetna's presidency due to ill health in 1879, Bulkeley became the company's third president. In 1880, Bulkeley ran for both mayor of Hartford and governor of Connecticut. He lost the gubernatorial race but won the mayoral race and was Hartford's mayor from 1880 to 1888. As mayor he became known for his flamboyant generosity; for instance, arranging steamboat trips on the Connecticut River for underprivileged children, using his own money.  While mayor of Hartford, on February 11, 1885, Bulkeley married Fannie Briggs Houghton in San Francisco, California. They had two sons and a daughter.  In 1888, Bulkeley again ran for governor. In the election, Luzon B. Morris accumulated more votes than Bulkeley but neither had the required 50%. In accordance with the rules of the time, the General Assembly decided the winner and the largely Republican body chose Bulkeley. Although he did not run in 1890, the vote was so close and fell into such disarray due to ballot irregularities in Bridgeport that officials did not certify the results, and the Connecticut House of Representatives and Senate, each led by opposing parties, could not agree on a legal successor. When Bulkeley refused to recognize the Democratic candidate as the victor, the Democratic state comptroller changed the lock on an anteroom that led from the governor's office to the Statehouse. When Bulkeley found the door locked the next morning, he broke in with a crowbar, earning the nickname the "Crow-Bar Governor". When the legislature refused to appropriate money for state government operations because of the deadlock, Bulkeley, who also happened to be president of Aetna Life Insurance Co., had his company pick up the state's bills until the next election. Bulkeley remained in office two more years, and the state Supreme Court unanimously held that he had been the lawful governor for the disputed period of time.  Bulkeley later served one term in the U.S. Senate from 1905 to 1911, as part of the "Millionaires' Senate" of 1906, so named for the wealth of its members.

What role did he have in the U.S. Senate?
as part of the "Millionaires' Senate" of 1906, so named for the wealth of its members.