[1] In 1933, Bachmann was promoted to D.Phil with a thesis titled, Studies on the foundation of arithmetic with special reference to Dedekind, Frege, and Russell (German: Untersuchungen zur Grundlegung der Arithmetik mit besonderer Beziehung auf Dedekind, Frege, und Russell).

They had a son together, Sebastian[1] In 1935, Bachmann moved to the University of Marburg where assisted Kurt Reidemeister.

[1] After the war, Bachmann worked with the mathematician Karl-Heinrich Weise to rebuild the mathematics department at the University of Kiel.

From 1960 Bachman was editor of the series titled, Grundzüge der Mathematik für Lehrer an Gymnasien sowie für Mathematiker in Industrie und Wirtschaft (Basic features of mathematics for teachers at grammar schools as well as for mathematicians in industry and business).

[1] In 1962–1963, Bachmann was elected Dean of the mathematics department of the Faculty of Philosophy of Kiel University.