Phosphorene, a monolayer of black phosphorus, is promising for nanoelectronic applications not only because it is a natural p-type semiconductor but also because it possesses a layer-number-dependent direct bandgap (in the range of 0.3 to 1.5 eV). On basis of the density functional theory calculations, we investigate electronic properties of the bilayer phosphorene with different stacking orders. We find that the direct bandgap of the bilayers can vary from 0.78 to 1.04 eV with three different stacking orders. In addition, a vertical electric field can further reduce the bandgap to 0.56 eV (at the field strength 0.5 V/Å). More importantly, we find that when a monolayer of MoS2 is superimposed with the p-type AA- or AB-stacked bilayer phosphorene, the combined trilayer can be an effective solar-cell material with type-II heterojunction alignment. The power conversion efficiency is predicted to be ∼18 or 16% with AA- or AB-stacked bilayer phosphorene, higher than reported efficiencies of the state-of-the-art trilayer graphene/transition metal dichalcogenide solar cells.