  We report a multiband transport study of bilayer graphene at high carrier
densities. Employing a poly(ethylene)oxide-CsClO$_4$ solid polymer electrolyte
gate we demonstrate the filling of the high energy subbands in bilayer graphene
samples at carrier densities $|n|\geq2.4\times 10^{13}$ cm$^{-2}$. We observe a
sudden increase of resistance and the onset of a second family of Shubnikov de
Haas (SdH) oscillations as these high energy subbands are populated. From
simultaneous Hall and magnetoresistance measurements together with SdH
oscillations in the multiband conduction regime, we deduce the carrier
densities and mobilities for the higher energy bands separately and find the
mobilities to be at least a factor of two higher than those in the low energy
bands.
