We analyze the spectroscopic features of bilayer graphene determined by the formation of pairs of low-energy and split bands in this material. We show that the inter-Landau-level absorption spectrum in bilayer graphene at high magnetic field is much denser in the far-infrared range than that in monolayer material and that the polarization dependence of its lowest-energy peak can be used to test the form of the bilayer ground state in the quantum Hall-effect regime.