Bunce taught at Seton Hall University from 1947 to 1949 before joining the history faculty at St. John's in 1949, where he remained until his retirement.

He was a proponent of the "Imperial school" of historians who believed that one needed to study the American colonies as part of the larger British Empire.

He contributed five articles on British history to Catholic Encyclopedia for School and Home (McGraw-Hill, 1965), and a chapter ("Rockingham, Shelburne, and the Politics of Reform, 1779-1780") in Gaetano L. Vincitorio (ed.

[3] He also co-edited (along with Richard P. Harmond) Long Island as America: A Documentary History to 1896 (Kennikat Press, 1977).

He was buried in Holy Cross Cemetery in Brooklyn, New York on December 30, 2015, in the family grave with his parents, Ralph and Sarah (Sadie) Bunce.