  We present an experimental study of the infrared conductivity, transmission,
and reflection of a gated bilayer graphene and their theoretical analysis
within the Slonczewski-Weiss-McClure (SWMc) model. The infrared response is
shown to be governed by the interplay of the interband and the intraband
transitions among the four bands of the bilayer. The position of the main
conductivity peak at the charge neutrality point is determined by the
interlayer tunneling frequency. The shift of this peak as a function of the
gate voltage gives information about less known parameters of the SWMc model,
in particular, those responsible for the electron-hole and sublattice
asymmetries. These parameter values are shown to be consistent with recent
electronic structure calculations for the bilayer graphene and the SWMc
parameters commonly used for the bulk graphite.
