Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurcations organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures.