The utility of ultrasound imaging and therapy with microbubbles may be greatly enhanced by determining their impulse-response dynamics as a function of size and composition. Prior methods for microbubble characterization utilizing high-speed cameras, acoustic transducers and laser-based techniques typically scan a limited frequency range. Here, we report on the use of a novel photoacoustic technique to measure the impulse response of single microbubbles. Individual microbubbles are driven with a broadband photoacoustic wave generated by a nanosecond-pulse laser illuminating an optical absorber. The resulting microbubble oscillations were detected by following transmission of a second laser as it passes twice through the microbubble. The system could even resolve oscillations resulting from a single-shot. As a proof-of-concept study, the size-dependent, linear impulse response of lipid-coated microbubbles was characterized using this technique. This unique method of microbubble characterization with exceptional spatiotemporal resolution opens new avenues for capturing and analyzing microbubble system dynamics.