A physical mechanism driving the resistance switching in heterocontacts, formed by a metal counterelectrode and electrically conducting bulk perovskite manganites, is discussed. The nature of the inelastic, charge-hopping transport inside insulating and strongly inhomogeneous metal/manganite interfaces is studied theoretically. Comparison with measured current-voltage characteristics for a La0.67Ca0.33MnO3/Ag heterostructure in a high-resistance state reveals the presence of one or more charge traps along a conduction path within the interface. In a low-resistance state the main charge-transferring events are direct tunneling ones. The analysis of electrical noise measurements for a La0.82Ca0.18MnO3 single crystal in three different charge-transport regimes shows scattering centers with a broad, flat spectrum of excitation states, independent of manganite electrical and/or magnetic characteristics. All of these results are consistent with an oxygen-drift model for a bistable resistance state in perovskites.