The sixteen different high-symmetry stacking configurations in buckled honeycomb AsP bilayers were identified using block diagrams and studied through several high-level computations, including the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation (ACFDT-RPA). The lowest-lying energy form is an AA-type stacking, which is an indirect bandgap semiconductor, according to the G₀W₀ approach. All bilayers are indirect wide bandgap semiconductors, except for two systems, a narrow bandgap semiconductor and one with metallic behavior. This study shows the richness of structural and electronic properties in AsP hetero-bilayers with configurations found over a broad spectrum of interlayer distances and bandgaps.