Taylor, known by the nickname "Our Bob", was a native of Carter County, Tennessee and was a Democrat, a relatively rare affiliation for a native of that part of northeastern Tennessee. He was both admitted to the bar and elected to the U.S. House of Representatives in 1878, winning one term but failing to be reeelected in 1880. He was again a Democratic congressional nominee in 1882 and again defeated. He was first nominated by the Democrats for governor in 1886. Somewhat surprisingly, his Republican opponent was his older brother, Alfred A. Taylor. The subsequent campaign is known in Tennessee history as The War of the Roses after the conflict in English history of that name and the fact that Bob's supporters wore white roses, Alf's red. The two men travelled the state together, debating publicly at every stop and often sleeping at night in the same bed. Bob Taylor won election and was elected to a second term in 1890 and a third, non-consecutive term in 1896. (Alf was eventually elected governor himself in 1920, years after Bob's death.) Bob Taylor was also a newspaper publisher (co-founder of the Johnson City Comet) and one of the most famous and charismatic lecturers in the United States in between his stints as an elected official.

The most notable event of Taylor's final term as governor was the Tennessee Centennial Exposition, a World's Fair held in Nashville's Centennial Park, which was developed for the occasion, in the summer of 1897. (Tennessee's actual centennial as a state was in 1896, but it had become apparent early on to the organizers that they were not going to be able to put the event together in a timely manner, and hence they postponed it for a year.) Unlike most such events, it was something of a financial success in that it succeeded in essentially breaking even (with a reported profit of under $50!). This event is probably most remembered today as the origin of Nashville's unique full-sized reproduction of the Athenian Parthenon.

The most unfortunate aspect of Taylor's administration was probably the increase in the poll tax, which served to disenfranchise poorer Tennesseans even further. An early attempt at statewide Prohibition was repealed during his term; however, this issue was certainly to surface again later. Years after his final term as governor he was elected to the United States Senate by the state legislature, the method used prior to ratification of the Seventeenth Amendment in 1913. He served in that office from 1907 until his death in 1912. In 1910, when incumbent Democratic governor Malcolm R. Patterson withdrew from his contest for reelection due to the turmoil created within the party over the Prohibition issue, he agreed to serve as a replacement nominee. He was defeated by Republican nominee Ben W. Hooper, who had previously defeated Alf Taylor for the Republican nomination. This is a rare example of two brothers being defeated by the same opponent in the same year but in different races. Following his defeat in the gubernatorial race, Taylor continued to serve in the Senate until his death less than two years later. He was originally buried at Old Gray Cemetery in Knoxville, but his remains were subsequently disinterred in 1938 and reburied at Monte Vista Cemetery in Johnson City in a family plot adjacent to his brother Alf.