Bunch was born on August 7, 1925 on a farm outside Lowry City, Missouri. He graduated from Central Missouri State University with a Bachelor of Science degree, then received a master's degree in English from Washington University in St. Louis. He pursued a Ph.D in English Literature at Washington University and the State University of Iowa, but rather than completing his doctoral dissertation, he shifted to creative writing and studied for two years at the Iowa Writers' Workshop before dropping out.