Biohybrid bacteria-based microrobots are increasingly recognized as promising externally controllable vehicles for targeted cancer therapy. Magnetic fields in particular have been used as a safe means to transfer energy and direct their motion. Thus far, the magnetic control strategies used in this context rely on poorly scalable magnetic field gradients, require active position feedback, or are ill-suited to diffuse distributions within the body. Here, we present a magnetic torque-driven control scheme for enhanced transport through biological barriers that complements the innate taxis toward tumor cores exhibited by a range of bacteria, shown for Magnetospirillum magneticum as a magnetically responsive model organism. This hybrid control strategy is readily scalable, independent of position feedback, and applicable to bacterial microrobots dispersed by the circulatory system. We observed a fourfold increase in translocation of magnetically responsive bacteria across a model of the vascular endothelium and found that the primary mechanism driving increased transport is torque-driven surface exploration at the cell interface. Using spheroids as a three-dimensional tumor model, fluorescently labeled bacteria colonized their core regions with up to 21-fold higher signal in samples exposed to rotating magnetic fields. In addition to enhanced transport, we demonstrated that our control scheme offers further advantages, including the possibility for closed-loop optimization based on inductive detection, as well as spatially selective actuation to reduce off-target effects. Last, after systemic intravenous injection in mice, we showed significantly increased bacterial tumor accumulation, supporting the feasibility of deploying this control scheme clinically for magnetically responsive biohybrid microrobots.