The optical absorption properties of bilayer zigzag-edge graphene nanoribbons (BL-ZGNRs) with external transverse electric fields are investigated by taking into account the Coulomb interaction effect in the Hartree-Fock approximation. We study the phase transitions of BL-ZGNRs induced by external electric fields and also the optical selection rules for the incident light polarized along the longitudinal and transverse directions. We find that the excitations from the edge states are crucial for the optical properties of BL-ZGNRs in the antiferromagnetic phase. We show that the low energy part of the optical absorption can be modulated by the external transverse electric field, and there is a broad band low frequency absorption enhancement for the transverse-polarized incident light in the charge-polarized state of BL-ZGNRs.