Bradley graduated from Mineral Wells High School in 1965 and attended Midwestern University (now Midwestern State University) in Wichita Falls as a member of the Honors Program, graduating with a B.A. in English in 1969. At Midwestern, he was student body president, editor of The Wichitan (the student newspaper), and an award-winning intercollegiate debater. At Texas Christian University in Fort Worth, he earned an M.A. in 1973 and Ph.D. in 1975 in English. At TCU he was a resident advisor in the athletic dormitory for two years, and, for two more years, he was head resident of the Tom Brown Dormitory Living-Learning Experiment. He also won the inaugural student writing contest sponsored by the Texas Association of Creative Writing Teachers (TACTT).

After graduating from TCU, Bradley embarked on a distinguished career as a university professor, administrator, scholar, and poet. He began his career as an assistant professor at Boston University, then moved to New Mexico Tech, where he became chair of the Department of Humanities. At New Mexico Tech he co-founded (with Prof. John Rothfork) and edited for seventeen years New Mexico Humanities Review, which became one of the most distinguished journals of Southwestern letters. He also published his first volume of poetry, Simple Versions of Disaster (University of North Texas Press, 1991), a collection that was greeted with wide acclaim.

In 1993 Bradley became Dean of Humanities at Indiana University Southeast before returning to Texas to chair the Department of English at West Texas A&M University in Canyon. Six years later in 1999, he was inducted into the prestigious Texas Institute of Letters and later served on its executive council. Besides teaching classes and overseeing remarkable growth in the department, he was an active member of Panhandle Professional Writers and founded the West Texas A&M summer writing program which drew students and writers from across the state for two weeks of intensive literary activity. He continues his voluntary service since 1999 as poetry editor of Concho River Review, a literary journal sponsored by the English Department at Angelo State University.

After seven years at West Texas A&M, Bradley became Dean of Graduate Studies, Associate Vice-President of Research, Director of International Programs, and Professor of English at Lamar University in Beaumont, where he continues to teach and write. Additionally, he continues to be active in several professional organizations in which he has served as poetry and creative writing chairman (Popular Culture Association) and president (Southwest Popular and American Culture Association and the Conference of College Teachers of English).

In 2018 Bradley received the Leland Best Distinguished Faculty Fellow Award from Lamar University. He received the Margie Boswell Poetry Award from TCU in 2017. The Minnie Stevens Piper Foundation in 2014 named him one of the top ten professors in Texas. Also in 2014, he received the Ann Die Hasselmo Faculty Excellence Award at Lamar. In 2009 he received the inaugural Distinguished Leadership Award from the Southwest Popular and American Culture Association. Bradley has received more than forty grants in support of literary activities, including ones from the National Endowment for the Arts, the Witter Bynner Poetry Foundation, and the New Mexico Arts Division.

He is married to the architectural historian Barrie Scardino Bradley.