Novel target materials with anisotropic response will play a key role in detecting low-mass dark matter in upcoming experiments. Bilayer graphene is one such material that has been proposed for the detection of sub-MeV mass dark matter particles via electronic excitations. In this work, we calculate scattering rate via a massive mediator in bilayer graphene. With an exposure as small as ~0.5 mg-year, bilayer graphene can probe new regions of the parameter space. The anisotropic response function of bilayer graphene leads to a sidereal-day modulation in the scattering rate, depending on its orientation with respect to the Galactic dark matter wind. We find significant modulation in the scattering rate for sub-MeV mass dark matter, demonstrating bilayer graphene’’s promise for a future experiment. We hope that our work will motivate the community to investigate bilayer graphene as a novel target material, and that it may lead us to discover the particle nature of dark matter.