Although he lost his bids to become a member of the U.S. Congress and to serve as New York State Governor, Aldridge was a well-known Republican party boss in Rochester and greater New York. During the Republican administration of Governor Charles Seymour Whitman, he was a member of Whitman's "Kitchen Cabinet" and was part of a triumvirate, known as the "Big Three" that once ruled the state with Thomas C. Platt (a U.S. Senator and U.S. Representative) and Francis Hendricks (a New York State Assemblyman, Senator and Mayor of Syracuse). The triumvirate later became the "Big Four" of Republican state politics with only Aldridge remaining alongside U.S. Representative William L. Ward, Fred Greiner (veteran of Erie County), and James Wolcott Wadsworth Jr. of Western New York. In 1888, he became a member of the New York Republican State Committee and soon thereafter was placed on the Executive Committee which he served on until his death. Aldridge was a delegate to the Republican National Conventions of 1896, 1900, 1904, 1908, 1912, 1916 and 1920 where he put forth the name of his friend, Warren G. Harding, who was later elected president.