Boltzmann transport theory fails near the linear band crossing of single-layer graphene and near the quadratic band crossing of bilayer graphene. We report on a numerical study which assesses the role of interband coherence in transport when the Fermi level lies near the band-crossing energy of bilayer graphene. We find that interband coherence enhances conduction, and that it plays an essential role in bilayer graphene's minimum conductivity phenomena. This behavior is qualitatively captured by an approximate theory which treats interband coherence in a relaxation-time approximation. On the basis of this short-range-disorder model study, we conclude that electron-hole puddle formation is not a necessary condition for finite conductivity in bilayer graphene at zero average carrier density.