Observations by Magnetospheric Multiscale have demonstrated that magnetic reconnection occurs at Earth's bow shock, typically at thin current sheets arising from plasma instabilities and turbulence in the shock transition region. Observational surveys of both the shock transition and the magnetosheath downstream suggest that the number of current sheets in these regions may not be strongly dependent on the shock Mach number MA or the angle between the upstream magnetic field and shock normal ( θBn). This result is somewhat surprising given that quasi-parallel and high Mach number shocks tend to have a more disordered and non-stationary structure. In order to investigate how shock reconnection manifests across different parameters, we perform a series of hybrid (fluid electron, kinetic ion) particle-in-cell simulations across a range of Mach numbers and orientations. Given that hybrid simulations cannot resolve electron-scale current sheets and reconnection, these simulations isolate an ion-scale mechanism for shock reconnection driven by an ion–ion beam instability in the foot. We find that this mechanism is strongly constrained to quasi-parallel shocks across all simulated Mach numbers. By quantifying reconnection using the area occupied by plasma on closed magnetic field lines, we find the number of reconnecting structures and closed field area increase with MA and decrease with θBn in the upstream and ramp regions. Downstream of the shock, however, we find a similar result to observational surveys: within the subset of quasi-parallel shocks, the decay rate of the closed field area (and hence thin current sheets) is not strongly dependent on upstream shock parameters.