He succeeded Johan Christian Fabricius as chief physician at Frederick's Royal Hospital in 1775.
He was the father of medical doctor Ole Bang, stepfather of bishop Jacob Peter Mynster and uncle of N.F.S.
He lived with his brother Oluf Lundt Bang, who was Attorney General and 16 years his senior, after the father's death.
In 1770, with the help of the Fincke's travel stipend and support from his brother, he was able to undertake a two-year trip abroad with stays in Berlin, Strasbourg and Paris.
Shortly after returning home, on 24 February 1773,. he defended his dissertation on the medical use of vitriolic acid, which he had prepared abroad.
[1] During the British bombardment of Copenhagen in 1807, his professor's residence (Fiolstræde 4–6) burned and with it his books, papers and the diary he had kept for many years.
Bang's home at Frederik's Hospital was one of the meeting places for the youth people who would later become of great importance to Denmark's spiritual life at the turn of the century.
Grundtvig and Henrik Steffens were Bang's nephews, and through O. H. Mynster, the latter came into contact with the young Adam Oehlenschläger.