Transition metal dichalcogenides (TMDs) have emerged as promising candidates for next-generation self-powered photodetectors due to their distinct optoelectronic properties, including strong light-matter interactions. However, their high exciton binding energies impede efficient exciton dissociation, hindering viable photodetector applications. This study, based on first-principles calculations, introduces a design approach featured by the asymmetrically enclosed structure of the TMD bilayer, i.e., two different self-assembled monolayers (SAMs) asymmetrically attached to each side of a tungsten diselenide bilayer by varying electron-donating and electron-withdrawing groups in SAMs. Compared to the electron-donating and electron-withdrawing tendencies, we demonstrate that the surface work function of the SAM is a crucial macroscopic parameter in fine-tuning the band offset without trap formation with a large degree of freedom. Optimizing the work function achieves trap-free exciton dissociation, establishing a type-II band alignment and a sufficient built-in electric field within the bilayer. This design approach offers not only a design strategy for two-dimensional (2D) self-powered photodetectors but also a guide to interface engineering of TMDs utilizing SAMs for integration into low-power applications.