There has been recent interest in superconductor-magnetic insulator hybrid Rashba nanowire setups for potentially hosting Majorana zero modes at smaller external Zeeman fields. Using the non-equilibrium Green’s function technique, we develop a quantum transport model that accounts for the interplay between the quasiparticle dynamics in the superconductor-magnetic insulator bilayer structure and the transport processes through the Rashba nanowire. We provide an analysis of three-terminal setups to probe the local and non-local conductance in clean and disordered nanowires. We uncover the gap closing and reopening followed by the emergence of near-zero energy states, which can be attributed to topological zero modes in the clean limit. In the presence of a disordered potential, trivial Andreev bound states may form with signatures reminiscent of topological zero modes. Our results provide transport-based analysis of regimes that support the formation of Majorana modes in these hybrid systems while investigating the effect of disorder on devices.