We report a fundamental study of single cavitation bubbles inside quasi-spherical water drops produced in microgravity (42nd ESA parabolic flight campaign, 8th ESA student parabolic flight campaign). High-speed imaging revealed implications of isolated, finite liquid volumes and spherical free surfaces on the bubble collapse and subsequent phenomena. In particular, bubble lifetimes in drops are shorter than in extended volumes in remarkable accordance with herein derived corrective terms for the Rayleigh-Plesset equation. We provide a physical interpretation of those terms and use the novel theory to make a general prediction of bubble collapse times in spherical liquid volumes. In the case of eccentrically placed bubbles, the toroidal collapse induces two liquid jets, consistent with theoretical predictions. They escape from the drop in antipodal directions and represent the first direct, simultaneous visualization of both cavity-related jets in a steady liquid volume.