We present data from molecular dynamics simulations concerning the nonstationary response of polymer brush bilayers to shear inversion. Bilayers with implicit solvents, dimeric solvents, and colloidal inclusions are subject to a quasi-instantaneous inversion of the shear direction, which mimics a highly nonstationary process. While we notice that the presence of an explicit solvent is essential to reproduce the experimentally observed mechanical instabilities, in particular an overshoot in the shear force, we also find that colloidal inclusions are capable of diminishing or even completely suppressing the instabilities. Our numerical data are complemented by scaling theory, where we determine a characteristic time scale that characterizes the response shortly after the inversion. In terms of chain length, N, shear rate, (gamma) over dot and distance between the grafting planes, D, we obtain tau similar to N/D(gamma) over dot(0.73) as the characteristic time, which is found to be in very good agreement with our numerical data. Our theory allows for predicting conformational and collective responses to shear inversion from static properties of the bilayer.