Differential scattering cross-section data have been measured at 43 angles from 11 • to 160 • for 37-MeV neutrons incident on 209 Bi. The primary motivation for the measurements is to address the scarcity of neutron scattering data above 30 MeV and to improve the accuracy of optical-model predictions at medium neutron energies. The high-statistics measurements were conducted at the China Institute of Atomic Energy using the 3 H(d,n) 4 He reaction as the neutron source, a pulsed deuteron beam, and time-of-flight (TOF) techniques. Within the resolution of the TOF spectrometer, the measurements included inelastic scattering components. The sum of elastic and inelastic scattering cross sections was computed in joint optical-model and distorted-wave Born approximation calculations under the assumption of the weak particle-core coupling. The results challenge predictions from well-established spherical optical potentials. Good agreement between data and calculations is achieved at 37 MeV provided that the balance between surface and volume absorption in a recent successful model [A. J. Koning and J. P. Delaroche, Nucl. Phys. A 713, 231 (2003)] is modified, thus suggesting the need for global optical-model improvements at medium neutron energies.