The NCAA began its investigation in 1982. Charley Pell admitted wrongdoing the summer of 1984, but he asked to stay on until the end of the season. In that summer, any player that wanted to transfer out or switch commitments, did transfer or change commitments. The Gators lost a couple high profile recruits, including two QBs. Somewhere around game three of the season, the NCAA told the school president, Marshal Criser, that the problem was a lot bigger than what Pell had let on. It was not a dozen infractions--it was over a hundred! Pell was immediately fired, and the NCAA immediately started the sanction process, which included immediate DQ from a post-season bowl game. Note that the Gators were still named national champs by several polls, including the New York Times. In December 1984, immediately after the 1984-1985 season ended, the SEC university presidents voted to strip Florida of its SEC title. The NCAA did not levy its scholarship punishments until January 1985--they banned Florida from TV for two years and reduced scholarships for the next three.
In short: there was no bowl game in 1984-1985 because the NCAA had preliminary findings in 1983-1984, with actionable evidence by game three of 1984.