Bostick played his high school ball in the tough AA section of Pennsylvania's WPIAL, the largest section in the state, at Jeannette High School. He was named to the Section AA First Team All-Star team his junior and senior years along and appeared on the AP All-State first team squad his senior year. He played in the Dapper Dan Roundball Classic, the first player in Jeannette history to do so, and led his team and the section in scoring and rebounding as he notched 21 points per game and hauled down 17 rebounds per contest. His 54 percent field goal average and 65 percent free throw average pointed out his excellent touch on the basketball.
Going into his freshman year, Coach Gardner thought that Bostick fit the bill of the new mold of players. Coach thought he was big, strong, lean, and extremely quick. Bostick appeared in 12 games that year and gained valuable playing time. He connected on 39.4 percent of his field goals as he averaged 2.4 points per game. He grabbed 14 rebounds and added three assists as he played both guard and forward. Sid was instrumental with his defensive efforts in some keys games his freshman year. Coach Gardener considered him the most improved player on the squad that year.
His sophomore year, Bostick went on to play in 27 games and averaged 4.7 points, 3.3 rebounds and handed out 25 assists. His role on the team evolved from his ability to run the Mountaineer offense well, to rebound and start the fast break. On defense, he was able to use his size and quickness to frustrate smaller or slower guards. As a junior, he started each of WVU's 29 games and finished third on the team in rebounding, averaging 6.3 board per game. That year, he also improved his free throw shooting average to 76.9 and won MVP honors at the Hall of Fame Tournament in Springfield, Massachusetts, when WVU captured the tourney title. Bostick scored 38 points and had 16 rebounds in those games against Syracuse and UMass, a career-high 22 against the Orangemen. Bostick also grabbed 16 rebounds in WVU's near upset of Rutgers that year. He ended up the year averaging 7.6 points and 7.3 rebounds in EAA games his junior year.