We investigate charge transport in disordered organic host–guest systems with a bimodal Gaussian density of states (DOS). The energy difference between the two Gaussians defines the trap depth. By solving the Pauli master equation for the hopping of charge carriers on a regular lattice with site energies randomly drawn from the DOS, we obtain the dependence of the charge-carrier mobility on the relative guest concentration, the trap depth, the energetic disorder, the charge-carrier density and the electric field. At small and high guest concentrations, our work provides support for recent semi-analytical model results on the dependence of the mobility on the charge-carrier density at zero field. However, at the cross-over between the trap-limited and trap-to-trap hopping regimes, where the mobility attains a minimum, our results can almost be one order of magnitude larger than predicted semi-analytically. Furthermore, it is shown that field-induced detrapping can contribute strongly to the electric-field dependence of the mobility. A simple analytical expression is provided which describes the effect. This result can be used in continuum drift-diffusion models for charge transport in devices such as organic light-emitting diodes.