Bergmann, who was born in Fuerth in Germany, studied in Munich and Berlin and gained his PhD under Emil Fischer in 1911. He worked as Fischer's assistant in Berlin until the latter's death in 1919. From 1921 to 1934 he was director of the Kaiser Wilhelm Institute for Leather Research, Dresden, from which he resigned on Hitler's coming to power. He then emigrated to America where he worked as a member of the Rockefeller Institute for Medical Research.

Bergmann's research interests were those of his teacher, Fischer: carbohydrates and amino acids. In 1932 he discovered the carbobenzoxy method of peptide synthesis, the greatest advance in this field since Fischer's first peptide synthesis in 1901. In this method the amino group of amino acids is ‘protected’ by the carbobenzoxy group during condensation to form the peptide linkage and later freed by hydrolysis. Following Bergmann's work, many other protective groups have been used in peptide syntheses.

In America Bergmann investigated the specificity of proteinase enzymes and discovered (1937) that enzymes like papain were capable of splitting quite small peptides at precise linkages. The last three years of his life were devoted mainly to problems connected with the war.