Bolin died in office on March 4, 1978. Although Mofford was Secretary of State, she held that post by appointment, so she could not ascend to the governorship; instead, Attorney General Bruce Babbitt became governor. At the end of the term she ran for a full term as Secretary of State and won. She was reelected in 1982 and 1986. In 1982 she won the election by nearly a 2-1 ratio, and won unopposed in 1986. Mofford became known in the state capital as the friendly woman with a beehive hairdo, and her office gained a reputation as an efficient operation. She herself was noted for her punctuality, answering her own phone and replying directly to her mail. In addition to her state position, she served from 1982 until 1983 as president of the National Association of Secretaries of State.