Based on first-principles density functional theory and nonequilibrium Green's function, we study the electronic band structures, the electronic transport properties, and the optical absorption of bilayer blue phosphorene nanoribbons (BPNRs). Both bilayer armchair BPNRs (a-BPNRs) and zigzag BPNRs (z-BPNRs) behave as semiconductors in the narrow nanoribbon case and metals in the wide nanoribbon case, sharply different from their monolayer counterparts where the monolayer a-BPNRs (z-BPNRs) are always semiconducting (metallic). This indicates that interlayer couplings or the increasing layer number may induce the switching of the conductivity of the monolayer BPNRs, which is absent in graphene and phosphorene nanoribbons. Furthermore, we explore the edge states of the energy bands near Fermi energy, and find that there are almost no pure edge-state band branches in the bilayer BPNRs, which can be attributed to the interlayer couplings between the edge-states in one layer and the bulk-states in the other. Consequently, the resulting complex band structures cannot be directly analyzed any more in the framework of the two-body coupling picture just according to the simple band structures of the monolayer BPNRs. Finally, we present the current-voltage characteristics and the optical absorption of the bilayer a-BPNRs and z-BPNRs. The influences of the nanoribbon width and the interlayer couplings on the current and the anisotropic optical absorption can be understood based on the complex energy band structures. This research should be an important reference of extending the field of BPNRs from the monolayer to the bilayer case, and deepen the understanding of the difference between the monolayer and bilayer nanoribbons in different materials.