  The inhomogenous real-space electronic structure of gapless and gapped
disordered bilayer graphene is calculated in the presence of quenched charge
impurities. For gapped bilayer graphene we find that for current experimental
conditions the amplitude of the fluctuations of the screened disorder potential
is of the order of (or often larger than) the intrinsic gap $\Delta$ induced by
the application of a perpendicular electric field. We calculate the crossover
chemical potential, $\Delta_{\rm cr}$, separating the insulating regime from a
percolative regime in which less than half of the area of the bilayer graphene
sample is insulating. We find that most of the current experiments are in the
percolative regime with $\Delta_{\rm cr}<<\Delta$. The huge suppression of
$\Delta_{\rm cr}$ compared with $\Delta$ provides a possible explanation for
the large difference between the theoretical band gap $\Delta$ and the
experimentally extracted transport gap.
