Direct measurements of individual bubble oscillations in lithotripsy fields have been performed using light-scattering techniques. Studies were performed with bubble clouds in gassy water as well as single levitated bubbles in degassed water. There is direct evidence that the bubble survives the inertial collapse, rebounding several times before breaking up. Bubble dynamics calculations agree well with the observations, provided that vapor trapping (a reduction in condensation during bubble collapse) is included. Furthermore, the afterbounces are dominated by vapor diffusion, not gas diffusion. Vapor trapping is important in limiting the collapse strength of bubbles, and in sonochemical activity.