Encapsulated microbubbles are well established as highly effective contrast agents for ultrasound imaging. There remain, however, some significant challenges to fully realize the potential of microbubbles in advanced applications such as perfusion mapping, targeted drug delivery, and gene therapy. A key requirement is accurate characterization of the viscoelastic surface properties of the microbubbles, but methods for independent, nondestructive quantification and mapping of these properties are currently lacking. We present here a strategy for performing these measurements that uses a small fluorophore termed a "molecular rotor" embedded in the microbubble surface, whose fluorescence lifetime is directly related to the viscosity of its surroundings. We apply fluorescence lifetime imaging to show that shell viscosities vary widely across the population of the microbubbles and are influenced by the shell composition and the manufacturing process. We also demonstrate that heterogeneous viscosity distributions exist within individual microbubble shells even with a single surfactant component.