Atomic layer materials with semiconducting electronic properties have attracted much attention as conducting channels in field-effect transistors (FETs). Here, we investigate the electronic structures of bilayer MoS₂ in a dual-gate FET model using first-principles total-energy calculations based on density functional theory (DFT). Our calculations show that selective electron doping occurs in bilayer MoS₂ under a perpendicular electric field owing to a band offset between the positive and negative-electrode sides of the MoS₂ layers. Furthermore, we observe a further partial carrier distribution in bilayer MoS₂ by decreasing the interlayer interaction owing to a twisted stacking arrangement. It is expected that the positive-electrode-side layer works as a conducting channel, and on the other hand, the negative-electrode-side layer works as a screening layer in bilayer MoS₂-FETs.