Ferroelectric materials attract much attention for applications in resistive memory devices due to the large current difference between insulating and conductive states and the ability of carefully controlling electronic transport via the polarization set-up. Bismuth ferrite films are of special interest due to the combination of high spontaneous polarization and antiferromagnetism, implying the possibility to provide multiple physical mechanisms for data storage and operations. Macroscopic conductivity measurements are often hampered to unambiguously characterize the electric transport, because of the strong influence of the diverse material microstructure. Here, we studied the electronic transport and resistive switching phenomena in polycrystalline bismuth ferrite using advanced conductive atomic force microscopy (CAFM) at different temperatures and electric fields. The new approach to the CAFM spectroscopy and corresponding data analysis are proposed, which allow deep insight into the material band structure at high lateral resolution. Contrary to many studies via macroscopic methods, postulating electromigration of the oxygen vacancies, we demonstrate resistive switching in bismuth ferrite to be caused by the pure electronic processes of trapping/releasing electrons and injection of the electrons by the scanning probe microscopy tip. The electronic transport was shown to be comprehensively described by the combination of the space charge limited current model, while a Schottky barrier at the interface is less important due to the presence of the built-in subsurface charge.