A career politician, Bradley's early years were marked by defeats in numerous elections for state and national office. His persistence eventually paid off however, as he was elected the first Republican governor of a heavily Democratic state, and became known as the father of the Republican Party in Kentucky. He was subsequently elected to the U.S. Senate, but his term was cut short by his death in 1914.
While Bradley was still young, the family moved to Somerset, Kentucky, where he was educated by private tutors and at a private school. He twice dropped out of school and ran away to join the Union Army during the Civil War; the first time being at fourteen years of age. Both times, he was returned to the care of his father.
In 1861, Bradley became a page in the Kentucky House of Representatives. It was during this service that his interest in both law and politics was born. He studied law under his father, one of Kentucky's leading criminal lawyers. Despite having no college education, Bradley was allowed to take the bar examination at age 18 by a special provision of the legislature. This arrangement was contingent on Bradley's being judged competent by two circuit judges. Bradley passed the exam, and was licensed in 1865, joining his father's firm in Lancaster.
On July 13, 1867, Bradley married Margaret Robertson Duncan. The couple had two children, George Robertson Bradley and Christine Bradley South. George's death at the age of twenty-four was a tremendous emotional blow from which Bradley never fully recovered.
In 1887, Bradley campaigned for Governor of Kentucky against Democrat Simon B. Buckner. Though he lost the election by more than 6,000 votes, he made the best showing of any Republican candidate for the office to that time, and garnered strong support from the state's black voters.
In 1888, Bradley received 105 votes for the Vice-Presidential nomination at the Republican National Convention. President Benjamin Harrison appointed him Minister to Korea in 1889, but he declined the job. From 1890 to 1896, he was a member of the Republican National Committee, and was the Kentucky delegation's choice for Presidential nominee in 1896.
During Bradley's term, Republicans controlled the Kentucky House of Representatives, while Democrats controlled the Kentucky Senate. This led to infighting between the two houses of the General Assembly and between the General Assembly and the governor. A prominent example of this deadlock played out in the senatorial election of 1895. Republican legislators nominated W. Godfrey Hunter; the Democrats chose J. C. S. Blackburn. The Republicans were joined by Gold Democrats who refused to back Blackburn, a free silver supporter. Attempts were made to unseat several legislators in the General Assembly, leading to threats of violence. Governor Bradley attempted to neutralize the situation by calling up the state militia, a move panned by the Democrats. The session adjourned with no decision. At a special session called by Bradley in March 1897, Republicans withdrew their nomination of Hunter and put forth William Joseph Deboe in his place. Deboe was elected on the 112th ballot, becoming the first Republican senator from the Commonwealth.
The election of Republican president William McKinley in 1896 deepened the Democrats' resolve to oppose the Republican governor and his allies, and further hindered progress during Bradley's administration. Bureaucratic delays contributed to the ineffectiveness of the four Kentucky regiments that fought in the Spanish-American War. Locally, Bradley struggled to end violent feuds that continued in the eastern part of the state. (The infamous Hatfield-McCoy feud had ended only a few years prior.) A compulsory education law and the Goebel Election Law both passed over Governor Bradley's veto, and a pure food and drug law passed without his signature. He did, however, successfully veto controversial legislation regulating railroad rates.
The election of Republican governor Augustus E. Willson in 1907 again emboldened Republicans in the General Assembly, who nominated Bradley for a seat in the U.S. Senate in 1908. The Democrats countered by nominating outgoing governor J. C. W. Beckham. Again, Bradley capitalized on divisions in the Democratic party, this time over the issue of Prohibition. After twenty-nine ballots, four Democrats who favored Bradley's "wet" position defied allegiance to their party, electing Bradley by a 64–60 margin.
During the Sixty-first and Sixty-second Congresses, Bradley was chairman of the U.S. Senate Committee on Expenditures in the Department of Justice. He was also chairman of the Committee to Investigate Trespassers upon Indian Land during the Sixty-first Congress, and the chairman of the Committee on Revolutionary Claims during the Sixty-third Congress.
Upon Bradley's death, both houses of Congress passed resolutions expressing their sympathy, and promptly adjourned out of respect. His body was returned to Frankfort, Kentucky for burial, but in accordance with the wishes of Bradley and his family, his body did not lie in state. He was buried in the state cemetery in Frankfort.