Born in Ann Arbor, Michigan, Bostic starred at his hometown Pioneer High School in Ann Arbor. 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. In college at the University of Michigan, Bostic started eight games in 1980, and he had an interception in the January 1, 1981 Rose Bowl for the 1980 Big Ten Conference Champions. This game was the first bowl game victory for Bo Schembechler. He started eleven games in 1981 and twelve in 1982. Bostic was first-team All-Big Ten for the 1982 Big Ten Champions who also went to the Rose Bowl. When he was drafted into the NFL, he was second on the modern Michigan career interceptions list (since 1965) with ten career interceptions, which places him in a tie for seventh on the list now. He ranks tenth on the All-time list. He ranks second on the All-time single-season fumble recovery list with four and fourth on the career list with six. His 119 interception return yards in 1982 ranks fifth all-time.
