We investigate the contribution of the low-energy electronic excitations toward the Raman spectrum of bilayer graphene for the incoming photon energy Ω≳1 eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field, due to the parabolic dispersion of the low-energy bands in a bilayer crystal, this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n−→n+ inter-Landau-level transitions with crossed polarization of in/out photons. We estimate the quantum efficiency of a single n−→n+ transition in the magnetic field of 10 T as In−→n+∼10−12.