While at Michigan, he accumulated fumble recovery and interception statistics that continue to rank among the leaders in school history.
[3] He then stayed in Ann Arbor to play for the University of Michigan where he earned four varsity letters in football from 1979 to 1982 while wearing the #13.
[4] In college at the University of Michigan, Bostic started eight games in 1980,[5] and he had an interception in the January 1, 1981 Rose Bowl for the 1980 Big Ten Conference Champions.
[17] Bostic's physical style of play was well-suited for Jerry Glanville who took over the Oilers' head coaching job for the 1986 NFL season after having been the team's defensive coordinator.
[22] That total led the American Football Conference (AFC),[23] and he added three quarterback sacks and a fumble recovery that season.
[12][24][26] Even after a surprise 1987–88 NFL playoff run the Oilers fired their defensive backs coach, Tom Bettis who had taken over from Ken Houston.
[28] That season, he finished tied for the third and final AFC safety Pro Bowl spot with David Fulcher and missed being invited due to the tiebreaker.
[33] The Indianapolis Colts signed Bostic as a plan B free agent to a two-year $900,000 contract,[34] but released him during training camp.
[40][41] He combined strength and speed to play his physical style according to Ozzie Newsome: "He's as strong as any linebacker and can run like any of the guys on the corner.
[44] At one point in Bostic's career, while Glanville was still defensive coordinator, the Oilers considered moving him to cornerback because of his speed.
[48] During one NFL training camp Bostic played with tape over his mouth to try to win a $20 bet with Steve Brown over who could keep from talking the longest.
[49] His son, Tony Bostic, played running back for the New Mexico State Aggies as a non-recruited walk-on.
[50][51][52] His younger son, William, followed his father's footsteps and played linebacker[53] for his alma mater, the University of Michigan.