In 1965, Brady joined the staff in Washington, D.C., of U.S. Representative Speedy O. Long of Louisiana's 8th congressional district, since disbanded. He worked for Long until 1971; after a failed gubernatorial campaign, Long left Congress in 1973 and became the LaSalle Parish district attorney. At the age of thirty-seven, Brady was elected in 1975 to the Louisiana House in the first ever nonpartisan blanket primary system held in Louisiana. From 1984 to 1987, he was the vice chair of the House Administration of Criminal Justice. He was also a member of the House Education Committee. In 1983, Brady survived a heated challenge from Democratic former Representative W. L. Rambo of Georgetown and sitting House member Richard S. Thompson of Colfax, both in Grant Parish. Brady led the primary field with 6,424 votes ; Rambo trailed with 5,185 ballots. Thompson garnered 4,960 votes, and the remaining 1,276 votes went to Darrel Glen Thaxton of Jena, another Democrat. Brady prevailed by 207 votes in the runoff election, 7,301 to 7,094 for Rambo. Without his strong support in La Salle Parish, Brady would have been defeated. In 1986, Brady challenged the incumbent, fellow Democrat Jerry Huckaby of Bienville Parish, for Louisiana's 5th congressional district seat, which Huckaby had held for a decade. Huckaby prevailed with 96,200 votes to Brady's 32,284 ballots, and 11,966 votes for the Monroe businessman Fred W. Huenefeld. Brady won only in La Salle Parish and only by 154 votes. In 1987, in his bid for a fourth term in reconfigured House District 22, Brady led in the primary against six other Democrats but was forced into a runoff election against A. Dale Smith, who trailed by about 1,500 votes. Smith prevailed in the second balloting, 8,111 to 6,893. Brady won only narrowly in his own LaSalle Parish and lost Grant and Rapides parishes.
Personal life
While serving in the legislature, Brady began working in the real estate appraisal business. After his House service, he relocated to Alexandria, where he opened Bud Brady Appraisals. He also had a passion for writing gospel and country music and played the dobro, an instrument given to him by former GovernorJimmie Davis. For a time, he went to Nashville, Tennessee, to pursue a musical career; there, he met Reba McEntire, but none of his songs were placed on an album. In 1960, Brady married Cullyne Roy Scott, whom he had met at NSU. A former schoolteacher, she resides in San Diego, California. Their son, Roderick Edward Brady, was killed in an accident while still a teenager. The Bradys had two daughters, Cecelia H. Brady, the Miss Louisiana USA in the 1986 pageant and subsequently a resident of San Diego, and Charlane R. Brady of Reykjavík, Iceland and San Francisco, California. He had two grandchildren. Brady was also survived by his brother, Gerald Brady of Lafayette, Louisiana, and a sister, Shirley B. Talley of Houston, Texas. Brady was a Southern Baptist while living in LaSalle Parish, but after he relocated to Alexandria, he became a Pentecostal. He died in Alexandria at the age of seventy-two. Services were held on April 8, 2011 at Forest Lawn Funeral Home in Ball, with interment at Forest Lawn Memorial Park north of Pineville. After Brady's death, the Louisiana State Senate approved a concurrent resolution, authored by Joe McPherson of Alexandria and Gerald Long of Natchitoches, to honor him for his public service. Oddly, another "Thomas Brady", from Terrebonne Parish in South Louisiana, preceded Bud Brady in the Louisiana House. Elward Thomas Brady, Jr., a businessman from Houma, served during the term from 1972 to 1976 but left the house to run unsuccessfully for the Louisiana State Senate at the same time that Budy Brady was first elected.