He studied in Los Angeles and played in 1945 with Shorty Sherock and Wingy Manone, and in 1948 with Dick Pierce.
Between 1950 and 1952, he worked extensively as a session musician with Nat King Cole, Maynard Ferguson, and Dexter Gordon.
In the middle of the 1950s, he played in Europe with Zoot Sims, Lars Gullin, Frank Rosolino, and Åke Persson.
Between 1956 and 1967, he again worked with Kenton and with Les Brown; toward the end of the 1950s, he also played with Jimmie Rowles, Shelly Manne, and Phil Woods.
In the 1970s and 1980s, Bagley composed and arranged for film and television, including the scores to Mama's Dirty Girls (1974), The Manhandlers (1974), The Swinging Barmaids (1975), The Student Body (1976), Young Lady Chatterley (1977) and Sacred Ground (1983).