Anne Evelyn Bunting was born in Maghera to Sloan Edmund Bolton, a postmaster, and Mary (née Canning) Bolton, a homemaker. She married business executive Edward Davison Bunting, whom she met in college, on March 26, 1950, and has three children: Christine, Sloan, and Glenn. She was educated in Belfast, Northern Ireland, attending Methodist College in the early 1940s and graduating in 1945; she then attended Queen's University, where she met her husband. After marrying, the couple moved to Scotland and started their family.
In 1958, Bunting immigrated to the United States with her husband and three children, later attending Pasadena City College in 1959. Bunting then enrolled in a community college writing course. She felt the desire to write about her heritage. Bunting's first published story, The Two Giants (1971), focused an Irish folktale about Finn McCool who out smarted Culcullan, a terrible Scottish giant. The first published work gave Bunting confidence and passion to pursue a writing career.
Bunting has taught writing classes at the University of California, Los Angeles and at various at writer's conferences. She is a member of International PEN and the Society of Children's Book Writers and Illustrators. She continues to write at her home in Pasadena, California, and has six grandchildren.