In 1974, Quivers graduated from the University of Maryland School of Nursing. Her first position was at the Maryland Shock Trauma facility of the Maryland Institute for Emergency Medical Services System, where she described her role as that of "a shock-trauma, intensive care kind of nurse, so I saw unpleasantness all the time". Knowing she could use her degree, Quivers joined the United States Air Force in July 1975, where she was commissioned as a second lieutenant. She entered active duty on January 11, 1976, before she was promoted to first lieutenant after six months of service. By June 1978, she had acquired the rank of captain. Quivers was discharged a month later, although she remained a member of the United States Air Force Reserve, with no active duty, until 1990.