Following graduation from law school, Bissell served as law clerk to Judge Arthur Stephen Lane of the United States District Court for the District of New Jersey from 1965 to 1966.

After his clerkship, Bissell entered private practice in Morristown, New Jersey from 1966 to 1969 before serving as an Assistant United States Attorney of the United States Attorney's Office for the District of New Jersey from 1969 to 1971.

[1] On November 23, 1982, President Ronald Reagan nominated Bissell to serve on the United States District Court for the District of New Jersey, to a seat vacated by Judge Vincent P. Biunno.

He was confirmed by the United States Senate on December 10, 1982 and received his commission the same day.

He retired on September 1, 2005, and returned to private practice, joining Connell Foley.