Robert F. Bennett was born 18 September 1933 in Salt Lake City, Utah, the youngest of five children of Wallace F. Bennett, the former four-term United States senator from Utah, and Frances Grant Bennett. He attended Salt Lake City's East High School and graduated from the University of Utah in 1957 with a degree in political science. There he participated in the Air Force ROTC program and served as student body president. In 1953-54 Bennett served as a missionary of the Church of Jesus Christ of Latter-day Saints in Scotland.
At age twenty-eight, Bennett managed his father's successful 1962 reelection campaign. That same year he married his long-time sweetheart, Joyce McKay. The Bennetts are the parents of six children. In 1962 Bennett served as press secretary for Representative Sherman P. Lloyd (R-Utah) and later served on an interim basis as his father's chief of staff.