He was an assistant professor at Princeton University until 1996, was twice a visiting professor at the University of Geneva (1992 and 2006), and was Professor of Mathematics at Imperial College London from 2002 to 2007. From 1993 to 2002 he was a Tutorial Fellow of Pembroke College, Oxford, and Reader (1996) then Professor of Topology (2000) in the University of Oxford. He remains a Supernumerary Fellow of Pembroke College.[7] In 2016, Bridson became only the second Manxman to ever be elected to the Royal Society, after Edward Forbes. In 2020, he was elected to Academia Europaea.[8] With André Haefliger, he won
the 2020 Steele Prize for Mathematical Exposition for the highly influential book Metric Spaces of Non-positive Curvature, published by Springer-Verlag in 1999.