  We study the collective modes of the quantum Hall states in undoped bilayer
graphene in a strong perpendicular magnetic and electric field. Both for the
well-known ferromagnetic state that is relevant for small electric field
$E_\perp$ and the analogous valley/layer polarized one suitable for large
$E_\perp$, the low energy physics is dominated by magnetoexcitons with zero
angular momentum that are even combinations of excitons that conserve Landau
orbitals. We identify a long wave length instability in both states, and argue
that there is an intermediate range of the electric field $E^{(1)}_\text{c} <
E_\perp < E^{(2)}_\text{c}$ where a gapless phase interpolates between the
incompressible quantum Hall states. The experimental relevance of this
crossover via a gapless state is discussed.
