We propose a new approach to microwave breast tumor sensing and diagnosis based on the use of biocompatible flagellated magnetotactic bacteria (MTB) adapted to operate in human microvasculature. It has been verified experimentally by Martel et al. that externally generated magnetic gradients could be applied to guide the MTB along preplanned routes inside the human body, and a nanoload could be attached to these bacterial microbots. Motivated by these useful properties, we suggest loading a nanoscale microwave contrast agent such as carbon nanotubes (CNTs) or ferroelectric nanoparticles (FNPs) onto the MTB in order to modify the dielectric properties of tissues near the agent-loaded bacteria. Subsequently, we propose a novel differential microwave imaging (DMI) technique to track simultaneously multiple swarms of MTB microbots injected into the breast. We also present innovative strategies to detect and localize a breast tissue malignancy and estimate its size via this DMI-trackable bacterial microrobotic system. Finally, we use an anatomically realistic numerical breast phantom as a platform to demonstrate the feasibility of this tumor diagnostic method.