Bates played college football at the University of Tennessee from 1979 through the 1982 season, where he was a four-year starter, the first two at free safety and the last two at strong safety. As a freshman in 1979, he registered 55 tackles (35 solo), 3 sacks, an interception, and 2 fumble recoveries. In 1980, he had 43 tackles (24 solo), including 3 tackles for a loss, to go along with an interception and 2 fumble recoveries. In 1981, he tallied 71 tackles (48 solo) and a team-leading 4 interceptions. During his senior year in 1982, he registered 86 tackles (61 solo), including 2 tackles for a loss, and 3 interceptions.