Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate in 1910. His dissertation was titled On the theory of automorphic functions (German: Theorie der automorphen Funktionen). He began working as a Privatdozent at Königsberg in 1910 and as Professor ordinarius at the University of Basel in 1913. He taught at the University of Frankfurt in 1915 and the University of Berlin from 1921 – 45.

Bieberbach wrote a habilitation thesis in 1911 about groups of Euclidean motions – identifying conditions under which the group must have a translational subgroup whose vectors span the Euclidean space – that helped solve Hilbert's 18th problem. He worked on complex analysis and its applications to other areas in mathematics. He is known for his work on dynamics in several complex variables, where he obtained results similar to Fatou's. In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic function to map the open unit disc injectively into the complex plane in terms of the function's Taylor series. In 1984 Louis de Branges proved the conjecture, which is now called de Branges' theorem. There is also a Bieberbach theorem on space groups. In 1928 Bieberbach wrote a book with Issai Schur titled Über die Minkowskische Reduktiontheorie der positiven quadratischen Formen.

Bieberbach was a speaker at the International Congress of Mathematicians held at Zurich in 1932.

Without being an active Nazi like Oswald Teichmüller, Bieberbach was, like Martin Heidegger, a fellow traveller and Nazi sympathizer. He was involved in the repression of Jewish colleagues, including Edmund Landau and his former coauthor Schur. Bieberbach was heavily influenced by Theodore Vahlen, another German mathematician and anti - Semite, who along with Bieberbach founded the "Deutsche Mathematik" ("German mathematics") movement and journal of the same name. The purpose of the movement was to encourage and promote a "German" (in this case meaning intuitionistic) style in mathematics. Bieberbach's and Vahlen's idea of having German mathematics was only part of a wider trend in the scientific community in Nazi Germany towards giving the sciences racial character, there were also pseudo - scientific movements for "German physics", "German chemistry", and "German biology". In 1945, Bieberbach was dismissed from all his academic positions because of his support of Nazism, but in 1949 was invited to lecture at the University of Basel by Ostrowski, who considered Bieberbach's political views irrelevant to his contributions to the field of mathematics.

"… the spatial imagination is a characteristic of the Germanic races, while pure logical reasoning has a richer development among Romanic and Hebraic races. … In the intellectual sphere the race shows in the manner of creation, the evaluation of the results, and I guess also in the standpoint considering foundational questions. … Formalism wants to build a realm of mathematical truths which is independent of man, whereas Intuitionism is based on the idea that mathematical thinking is a human endeavor and thus cannot be separated from man." (in Stilarten mathematischen Schaffens, i.e. Styles of mathematical creation / endeavour).