Bunker received the Humboldt Prize (1995), the Medaili Jana Marca Marci of the Czech Spectroscopy Society (2002), and the 2002 Sir Harold Thompson Memorial Award, which is sponsored by Pergamon Press (now Elsevier) for the most significant advance in spectroscopy published in Spectrochimica Acta each year. He is a fellow of the International Union of Pure and Applied Chemistry.