Pulsed laser deposited Au-BFO-Pt/Ti/Sapphire MIM structures offer excellent bipolar resistive switching performance, including electroforming free, long retention time at 358 K, and highly stable endurance. Here we develop a model on modifiable Schottky barrier heights and elucidate the physical origin underlying resistive switching in BiFeO3 memristors containing mobile oxygen vacancies. Increased switching speed is possible by applying a large amplitude writing pulse as the resistive switching is tunable by both the amplitude and length of the writing pulse. The local resistive switching has been investigated by conductive atomic force microscopy and exhibits the capability of down-scaling the resistive switching cell to the grain size.