With the help of numerical simulations in microscopic nonlinear quantum theory of coherent electromagnetic radiation interaction with a gapped bilayer graphene, we find the optimal values of pump wave intensity, graphene temperature, and energy gap induced by a constant electric field for practically significant third-order harmonic coherent emission. The Liouville-von Neumann equation is treated numerically for the third harmonic generation in multiphoton excitation regime near the Dirac points of the Brillouin zone. We examine the rates of the third harmonic at the particle–hole annihilation in the field of a strong pump wave of linear polarization for practically real/optimal parameters of a considering system. The obtained results show that by choosing the optimal values of the main characteristic parameters, a gapped bilayer graphene can serve as an effective medium for generation of the third harmonic at room temperatures in the terahertz and far-infrared domains.