We have conducted a comprehensive survey of burst mode observations of Earth's bow shock by the Magnetospheric Multiscale mission to identify and characterize current sheets associated with collisionless shocks, with a focus on those containing fast electron outflows, a likely signature of magnetic reconnection. The survey demonstrates that these thin current sheets are observed within the transition region of approximately 40% of shocks within the burst mode data set of Magnetospheric Multiscale. With only small apparent bias toward quasi-parallel shock orientations and high Alfvén Mach numbers, the results suggest that reconnection at shocks is a universal process, occurring across all shock orientations and Mach numbers. On examining the distributions of current sheet properties, we find no correlation between distance from the shock, sheet width, or electron jet speed, though the relationship between electron and ion jet speed supports expectations of electron-only reconnection in the region. Furthermore, we find that robust heating statistics are not separable from background fluctuations, and thus, the primary consequence of reconnection at shocks is in relaxing the topology of the disordered magnetic field in the transition region.