Bass was from Pulaski, Tennessee. He graduated from Martin Methodist College in Pulaski in 1941, and from 1947 to 1954, he was postmaster at Pulaski. In 1954, he was elected as a Democratic U.S. Congressman from Tennessee's 6th District, which included Pulaski. He was reelected four times and served until 1964, when Senator Estes Kefauver died in office. A Democratic primary was held for the unexpired balance of this term in August, 1964, and Bass entered this contest, surprising many by defeating Governor of Tennessee Frank G. Clement. In November, Bass defeated the Republican nominee, Howard Baker, to win the final two years of the term.

Since the election was for an unexpired term, and in the Senate seniority is a very important consideration when being considered for committee assignments, office assignments, and the like, Bass was sworn in as soon as the election results could be certified in order to give him a slight seniority advantage over other freshmen Senators elected in 1964. Bass became Tennessee's junior Senator (the senior Senator at that time being Albert Gore, Sr.) and prepared to run for a full term in 1966.

However, this race proved problematic for Bass. Clement still desired the seat for himself, especially since term limits were going to prevent him from standing to succeed himself as governor in 1966, and without this seat he would find himself out of politics, as he had once before when faced with term limits the first time in 1958. Bass hurt his own cause when, at a public social event, he very loudly and vociferously objected to being referred to by a nickname, "Bigmouth Bass". It was widely assumed (although never proven) that the stridency of this objection had been at least in part due to the influence of alcohol. Newspapers, particularly the Nashville Banner, had a field day with this event, as did, to a lesser extent, television. Bass lost the 1966 Democratic Primary to Clement that August. (Clement then proceeded to lose in the general election to Baker, who became Tennessee's first elected post-Reconstruction Republican Senator).

Bass subsequently made two attempts to re-enter politics. He ran for the 1974 Democratic nomination for governor but finished fifth in a nine-man field, a surprisingly weak finish for a former Senator. In 1976 he entered the Democratic primary for his former House seat and won the nomination. However, the district had been significantly redrawn since his previous service. Bass found himself running in a large amount of territory he did not know and that did not know him. In addition, much of this territory was heavily Republican, having been added by the state legislature after the 1970 census in an attempt to punish his successor in Congress, William Anderson for his perceived liberalism. He lost badly--by over 30 points--to Robin Beard, the Republican who had defeated Anderson, despite 1976 otherwise being almost a Democratic sweep in Tennessee, which voted for Jimmy Carter for President and saw the defeat of Senator Bill Brock in favor of Jim Sasser. Bass apparently saw that he had no future in elective politics. He later moved to Florida, where he lived until his death.

His brother, Horace Bass, is a former state Cabinet member and owner of a manufacturing firm in Nashville best-known for its line of mattresses.