In 1984, Bosco took over as starting quarterback at
Brigham Young University after
Steve Young graduated. In his first season as a starter, Bosco guided the
Cougars to a perfect 13–0 record. BYU finished the season by defeating
Michigan, 24–17, in the
Holiday Bowl, clinching the school's first and only
national championship. Despite injuries to his knee, ankle, and rib, he led the Cougars back from a 17–10 fourth quarter deficit. His 13-yard touchdown pass to Kelly Smith with 1:23 left in the game secured the victory. Bosco completed 283 of 458 passes for 3,875 yards and 33 touchdowns during the 1984 regular season. He led the nation in passing yardage, and finished second, behind
Doug Flutie of
Boston College, in pass efficiency. He finished third in the voting for the
Heisman Trophy. In Bosco's senior season (1985), BYU finished with an 11–3 record. He completed 338 of 511 passes for 4,273 yards (the second-highest total in BYU history at the time, behind
Jim McMahon's 4,571 yards in 1980), throwing 30 touchdown passes that year. Against
New Mexico, Bosco set a school single-game record by passing for 585 yards. He finished his BYU career with 10 NCAA records, ==Professional career==