We investigate the hopping transport of positively charged mobile oxygen vacancies V+o in electroforming-free bipolar memristive BiFeO3 switches by conducting impedance spectroscopy and quasistatic state-test measurements. We demonstrate that BiFeO3 switches with mobile oxygen vacancies (V+o ) and fixed substitutional Ti4+ donors on Fe3+ lattice sites close to the bottom electrode have a rectifying top electrode with an unflexible barrier height and a rectifying and/or nonrectifying bottom electrode with a flexible barrier height. The field-driven hopping transport of the oxygen vacancies determines the reconfiguration of the flexible barrier and the dynamics of the resistive switching. Average activation energies of 0.53 eV for trapping and of 0.31 eV for the release of oxygen vacancies by the Ti4+ donors during application of the SET and RESET excitation pulses are extracted, respectively. The larger activation energy during SET is experimentally verified by impedance spectroscopy measurements and evidences the local enhancement of the electrostatic potential profile at the bottom electrode due to the Ti4+ donors on Fe3+lattice sites.