Born in Helsen, Germany, Bier studied medicine in Leipzig and Berlin, graduating with high honours at Kiel in 1886. He was appointed assistant to the eminent surgeon von Esmarch and did valuable research into collateral circulations, which occur when a main blood vessel is blocked. In 1898, building on the work of Quincke who had introduced lumbar puncture, Bier injected cocaine into the spinal canal and reported six cases where he operated without pain on patients too weak for general anaesthesia.

To investigate the severe headache following spinal puncture, Bier and his assistant, Hildebrand, administered spinal anaesthetics to each other. Bier also introduced the technique of intravenous analgesia; injecting local anaesthetic into a vein of an exsanguinated limb below a tourniquet. This method is useful for ambulatory surgery.

After the death of the leading German surgeon von Bergmann in 1907, Bier was invited to replace him in Berlin. During World War I he was Consulting Surgeon to the German Army and introduced the steel helmet. In later life he became very interested in physical education and athletics. He was also an environmentalist and advocated the planting of forests.