Burbidge held several leadership and administrative posts, including Director of the Royal Greenwich Observatory (1973–75), President of the American Astronomical Society (1976–78), and President of the American Association for the Advancement of Science (1983). Burbidge worked at the University of London Observatory, Yerkes Observatory of the University of Chicago, the Cavendish Laboratory of the University of Cambridge, the California Institute of Technology, and the University of California San Diego (UCSD). From 1979 to 1988 she was the first director of the Center for Astronomy and Space Sciences at UCSD, where she worked from 1962 until her retirement.