We use speckle-visibility spectroscopy to measure the time dependence of bubble rearrangement events that are driven by coarsening in an aqueous foam. This technique gives the time trace for the average scattering site speed within a prescribed volume of the sample. Results are analyzed in terms of distributions of event times, event speeds, and event displacements. The distribution of rest times between successive events is also measured; comparison with diffusing-wave spectroscopy results shows that the spatial structure of a typical event consists of a core of only a few bubbles which undergo topology change plus a surrounding shell of bubbles which shift by an amount that decays to one wavelength at four to five bubbles away. No correlations are found between the durations, speeds, and rest times between successive events.