Daryle Hadley Busch was born to Dwight Hayes and Ione (Bauman) Busch in Carterville, Illinois. In 1951, Busch received a bachelor's degree in Chemistry and Mathematics from Southern Illinois University. In the following year, under the guidance of John C. Bailar, Jr., Busch received a master's degree from the University of Illinois. With Bailar's continued direction, Busch received his doctorate from the University of Illinois in 1954 with his thesis, "The Stereochemistry of Complex Inorganic Compounds."

Upon graduation, Busch became an assistant professor in inorganic chemistry at Ohio State University (OSU). Busch was promoted to an associate professor in 1959 and became tenured in 1963. During his career at OSU, Busch distinguished himself as a leader in the field of bioinorganic chemistry through his work with transition metal coordination chemistry. Many considered Busch one of the founding fathers of macrocyclic chemistry and the subject of ligand reactions. For his contributions to the field and his work as a professor, Busch was named a Presidential Professor at OSU in 1987.

In 1988, Busch relocated to the University of Kansas (KU) as the Roy A. Roberts Distinguished Professor of Chemistry. While at KU, Busch continued his work with inorganic chemistry and macrocyclic chemistry by researching further into complex molecular interactions. As part of his academic work at KU, Busch collaborated with Bala Subramanian to establish the KU Center for Environmentally Beneficial Catalysis (CEBC), a NSF Engineering Research Center, in 2003. Busch served in the role of Deputy Director. Busch is also the founder of the Busch Research Group, a group created to research transition metal coordination chemistry. Busch retired from KU in 2013.

With his academic work, Busch served in a number of professional institutions throughout his long career. From 1999 to 2001, Busch served on the Board of Directors at the American Chemical Society (ACS), including serving as president of the ACS in 2000. While serving as president of the ACS, Busch brought the Green Chemistry Institute (GCI) to the ACS and helped to establish the GCI's rules of operation within the ACS. Busch also served as Secretary of the Inorganic Division of the International Union of Pure and Applied Chemistry (IUPAC) and led the Commission on Nomenclature of Inorganic Chemistry (CNIC) at IUPAC. Busch was also active in the American Association for the Advancement of Science (AAAS), at one time serving as Chair of the Chemistry Division at AAAS.

Busch authored and coauthored over 400 scientific publications, including five books and 14 patents. Busch also received numerous awards in chemistry, including the ACS Award in Inorganic Chemistry (1963), ACS Award for Distinguished Service in the Advancement of Inorganic Chemistry (1976), the Dwyer Medal in Coordination Chemistry (1978), the Izatt-Christensen Award in Macrocyclic Chemistry, and the Alumni Teaching Award from OSU (1980). With his work as a professor and in the scientific community, Busch also consulted on various collaborations with a number of industrial companies, including DuPont, Monsanto, 3M, Air Products, and Proctor and Gamble.

In 1951, Busch married Geraldine Barnes. Geraldine and Daryle Busch had five children: Michael C. Busch, Steven J. Busch, Cheryl A. (Busch) Rome, Kristina M. (Busch) Rodriguez, and Derek H. Busch.