He studied at Loras College in Dubuque, from where he obtained a Bachelor of Arts degree in 1942. He completed his postgraduate studies at the Catholic University of America in Washington, District of Columbia
He was ordained to the priesthood on July 28, 1945. He then served as a teacher at Loras Academy until 1948, when he became secretary to Archbishop Henry Rohlman. In 1952 he earned his Doctor of Philosophy from Catholic University.
Returning to Iowa, he served as secretary to Archbishop Leo Binz (1952-1953) and superintendent of Catholic schools in the Archdiocese of Dubuque (1953-1967).
He was president of Loras College from 1967 to 1970. During his administration, he gave full scholarships to twelve African American students, who after meeting with Jesse Jackson in Chicago returned to Loras and demanded radical reforms from Driscoll.
He was eventually forced to expel the twelve students. The incident made him unpopular with the other faculty, who then sought his resignation.
He received his episcopal consecration on the following October 18 from Archbishop Luigi Raimondi, with Archbishops Leo Binz and James Joseph Byrne serving as co-consecrators.
He remained as bishop for the next fourteen years, until his death at age 64.
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Member Catholic Business Education Association (board directors), Alumni Association Theological College Catholic University American (1st vice president from 1965), National Catholic Education Association (executive board), Knights of Columbus (4th degree).