The microscopic quantum theory of nonlinear stimulated scattering of chiral particles in doped AB-stacked bilayer graphene on the Coulomb field of charged impurities in the presence of coherent electromagnetic radiation is presented. The Liouville–von Neumann equation for the density matrix is solved analytically. Here, the interaction of electrons with the scattering potential is taken into account as a perturbation. The absorption rate of nonlinear inverse-bremsstrahlung for a grand canonical ensemble of fermionic chiral particles is calculated using the obtained solution. The analysis of the obtained rate shows that from terahertz to the midinfrared range of frequencies there is significant absorption of incident radiation via multiphoton-stimulated bremsstrahlung mechanism.