Switchable beam steerers based on zenithal bistable liquid crystal (LC) gratings are designed and theoretically investigated. The nematic orientation profiles and the optical transmittance properties of the gratings are rigorously calculated, respectively, via a tensorial formulation of the Landau-de Gennes theory and the full-wave finite-element-method. By proper design of the grating geometry, beam steering with high diffraction efficiency is demonstrated between the two stable LC states. The tolerance of the device performance with respect to material parameters is assessed, evidencing spectral operation windows of more than 50 nm in the visible for a beam steering efficiency higher than 90%.