Plummer was born to Samuel Carl Plummer and Mabel Plummer in nearby Plumerville, a town named for his great-grandfather. He worked on Saturdays at Wiggs Flowers as a teenager. Plummer was a 1947 graduate of Plumerville High School and a 1951 graduate of Arkansas State Teachers College.
Plummer taught school at Nemo Vista in Center Ridge, and then at Corning High School. In the early 1950s he served in the Navy, rising to the rank of yeoman second class. After the war he taught elementary school in Long Beach, California. A trip home for his grandfather's funeral convinced him to return to his home state. He opened a florist's shop in Morrilton on February 1, 1958.
Plummer was 1964 president of the Arkansas Florist Association. He has continued as secretary-treasurer of that organization since 1966. Plummer chairs the board of Plumerville United Methodist Church to which he donated funds for a new fellowship hall in 1999. He served as mayor of Plumerville from 1998 to 2006. He sits on the UCA Alumni Board and the UCA Foundation Board. He established the William C. Plummer Scholarship at UCA for students in the College of Fine Arts and Communication.
- Amy Widner, "Bill Plummer," Arkansas Democrat-Gazette (River Valley & Ozark Edition), October 18, 2009.