We consider the dragging of fronts in reaction-diffusion systems with bistable nonlinearity by an external drive, which may be parametric or direct. A perturbation theory is developed for the speed correction of the dragged front. The predictions are found to be in good agreement with direct simulations, apart from an initial transient. While the perturbation theory should be valid for small values of the drive's strength E, the predictions are actually found to be quite accurate even for epsilon = O(1), and can quantify transitions between free and locked regimes of motion of the dragged fronts that occur at intermediate values of E.