We present a self-consistent calculation of the interlayer asymmetry in bilayer graphene caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally in [E.A. Henriksen, Z. Jiang, L.-C. Tung, M.E. Schwartz, M. Takita, Y.-J. Wang, P. Kim, and H.L. Stormer, Phys. Rev. Lett. 100 (2008), 087403]. We also analyse the magneto–optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers.