We analyze the response of bilayer graphene to an external transverse electric field using a variational method. A previous attempt to do so in a recent paper by Falkovsky [Phys. Rev. B 80, 113413 (2009)] is shown to be flawed. Our calculation reaffirms the original results obtained by one of us [E. McCann, Phys. Rev. B 74, 161403R (2006)] by a different method. Finally, we generalize these original results to describe a dual-gated bilayer graphene device.