For bilayer graphene in a magnetic field, we derive and solve a full set of
gap equations including all Landau levels and taking into account the
screened Coulomb interaction. There are two types of the solutions for the
filling factor $nu=0$: (i) a spin-polarized type solution, which is the ground
state at small values of perpendicular electric field $E_{perp}$, and (ii) a
layer-polarized solution, which is the ground state at large values of $E_
{perp}$. The critical value of $E_{perp}$ that determines the transition
point is a linear function of the magnetic field, i.e., $E_{perp,{rm cr}}=E_
{perp}^{rm off}+a B$, where $E_{perp}^{rm off}$ is the offset electric
field and $a$ is the slope. The offset electric field and energy gaps
substantially increase with the inclusion of dynamical screening compared
to the case of static screening. The obtained values for the offset and the
energy gaps are comparable with experimental ones.