  We re-examine the nature of the ground states of bilayer graphene at odd
integer filling factors within a simplified model of nearly degenerate $n=0$
and $n=1$ Landau levels. Previous Hartree-Fock studies have found that
ferroelectric states with orbital coherence can be stabilized by tuning the
orbital splitting between these levels. These studies indicated that, in
addition to a uniform ferroelectric state, a helical ferroelectric phase with
spontaneously broken translational symmetry is possible. By performing exact
diagonalization on the torus, we argue that the system does not have a uniform
coherent state but instead transitions directly from the uniform incoherent
state into the ferroelectric helical phase. We argue that there is a realistic
prospect to stabilize the helical ferroelectric state in bilayer graphene by
tuning the interlayer electric field in a model that includes all single
particle corrections to its zero energy eight-fold multiplet of Landau levels.
