Ferroelectric $$\hbox {BiFeO}_3$$ (BFO) thin films were deposited on (001) $$\hbox {SrTiO}_3$$ substrates buffered with $$\hbox {La}_{0.7}\hbox {Sr}_{0.3}\hbox {MnO}_3$$ (LSMO) electrodes. Bipolar resistive switching in Pt/BFO/LSMO heterostructures were observed with high stability and long retention. However, transport characteristics of Pt/BFO/LSMO is highly asymmetric and pronounced resistive switching can only be observed by applying negative reading pulses on the Pt top electrodes, i.e. when the Pt/BFO Schottky barrier is reverse-biased. This resistive switching is discussed in terms of a modulation on the Pt/BFO interface Schottky barrier by the polarization switching in ferroelectric BFO. Comparative studies on Pt/BFO/ $$\hbox {SrRuO}_3$$ and Pt/BFO/ $$\hbox {LaNiO}_3$$ heterostructures reveal that the work function of the electrode materials and the formation of Schottky barriers are significant to the observed resistive switching behaviors.