  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.
