Turbulent plasmas such as the solar wind and magnetosheath exhibit an energy cascade which is present across a broad range of scales, from the stirring scale at which energy is injected, down to the smallest scales where energy is dissipated through processes such as reconnection and wave-particle interactions. Recent observations of Earth's bow shock reveal a disordered or turbulent transition region which exhibits features of turbulent dissipation, such as reconnecting current sheets. We have used observations from Magnetospheric Multiscale (MMS) over four separate bow shock crossings of varying θ_Bn to characterise turbulence in the shock transition region and how it evolves towards the magnetosheath. We observe the magnetic spectrum evolving by fitting power laws over many short intervals and find that the power-law index in the shock transition region is separable from that of the upstream and downstream plasma, for both quasi-perpendicular and quasi-parallel shocks. Across the shock, we see a change in the breakpoint location between inertial and ion power-law slopes. We also observe the evolution of scale-independent kurtosis of magnetic fluctuations across the shock, finding a reduction of high kurtosis intervals downstream of the shock, which is more apparent in the quasi-perpendicular case. Finally, we adapt a method for calculating correlation length to include a high-pass filter, allowing estimates for changes in correlation length across Earth's bow shock. In a quasi-perpendicular shock, we find the correlation length to be significantly smaller in the magnetosheath than in the solar wind, however the opposite can occur for quasi-parallel shocks.