Burford was the daughter of Joseph Michael Egan and Mae Rene Flanary. She was educated at Bryn Mawr (Class of 1951), and SMU Graduate School (Class of 1954). She served as a teacher at the Norfleet School of Music and Individual Studies in New York, and was an instructor in the SMU English department after receiving her master's degree. She married poet William Skell Burford, who co-founded the literary magazine The Medusa. She died in Tarrant, Texas in 2002.