Information on the viscoelastic response to extensional deformation of polymeric solutions and other complex fluids is crucial for understanding their behavior in a wide variety of industrial applications. While the characterization of complex fluids using simple shear experiments is well established, a complete characterization of their extensional rheological properties is still challenging. Currently, methods such as CaBER, ROJER, and microfluidics are used for this. The downside of these techniques is that fluids with low viscosity and/or short relaxation times are still hard to characterize. Here we propose an alternative approach for measuring extensional rheological properties by using a microscopic air bubble as an extensional rheometer. We pursue this idea experimentally by submerging a single bubble in a pool of liquid and studying the dynamics of the bubble under influence of a change in hydrostatic pressure. This situation is analogous to a stress-controlled shear rheology experiment, where a time-dependent shear stress is applied to a sample and the resultant strain is measured. We test our approach on a range of polymeric fluids with different relaxation times and find that the bubble microrheology experiments provide results and trends that are indeed consistent with theoretical expectations and with previous data acquired using established methods. The concept of bubble microrheology is thus very promising. While the experimental technique is straightforward, practical improvements can still be made on the experimental setup and the data analysis, which could extend the range of investigable materials and the amount of information that can be extracted from the measurements. A chief advantage of our methodology is that it ensures the measurement of only extensional properties and that fluids with very short relaxation times can be measured. Finally, by applying a sinusoidal pressure variation instead of a pressure jump, our method could potentially be extended to oscillatory measurements.