Rensch was born in Thale and as a young boy, he took an interest in observing the natural world and discovered a talent for drawing and painting. He served in the German army from 1917–1920 and began to observe natural phenomena while he was held prisoner in France. He returned to Germany and began his studies on feather structure under Valentin Haecker who had himself studied under August Weismann. Until the 1930s Rensch held anti-Darwinian and Lamarckian views. Rensch also took an interest in the philosophy of science and was fascinated by Theodor Ziehen. Rensch also studied expressionist painting and in later life examined the biological roots of art. He received his Ph.D. from the University of Halle in 1922. He joined the zoological museum of the University of Berlin as an assistant in 1925. In 1927 he participated in a zoological expedition to the Sunda Islands. He studied the geographical distribution of subspecies of polytypic species and of complexes of closely related species with attention to how local environmental factors, especially climate, influenced their evolution. In 1929 he published the book Das Prinzip geographischer Rassenkreise und das Problem der Artbildung that discussed the relationship between geography and speciation. His work in this area would influence Ernst Mayr, who was also an assistant at the museum from 1927–1930, and would contribute to the development of the modern evolutionary synthesis. In 1937 he was forced to leave the museum because he refused to join the Nazi party, and took a position at a zoological garden in Münster. In 1940 he was recalled for military service, but was discharged for medical reasons in 1942. In 1947 he published a book that would later be translated into English under the title Evolution above the species level. The book discussed how the evolutionary mechanisms that drove speciation could also explain the differences between higher taxa. He introduced the concept of Artenkreis. It was considered a major document in the modern synthesis. That same year he became chairman of the zoology department and director of the zoological institute at the University of Münster. In 1953 he would take part in a zoological expedition to India. Later in his career he would work extensively in the areas of animal behavior, learning, and memory. Rensch also wrote on human behaviour and he suggested that the human evolutionary connection with organisms would lead to sympathy. He published an autobiography in 1979 and remained scientifically active until his death in 1990.
He was awarded the Linnean Society of London's prestigious Darwin-Wallace Medal in 1958. Since 2004, the Society for Biological Systematics has awarded the Bernhard Rensch prize for achievements of young scientists, writing in German or English, in the field of systematics and biodiversity research. A species of Indonesian lizard, Cryptoblepharus renschi, is named in his honor.