Tumor-targeting bacteria elicit anticancer effects by infiltrating hypoxic regions, releasing toxic agents and inducing immune responses. As the mechanisms of action of bacterial therapies are still to be completely elucidated, mathematical modeling could aid the understanding of the dynamical interactions between tumor cells and bacteria in different cancers. Here we propose a mathematical model for the anti-tumor activity of bacteria in tumor spheroids. We consider constant infusion and time-dependent administration of bacteria in the culture medium, and analyze the effects of bacterial chemotaxis and killing rate. We show that active bacterial migration towards tumor hypoxic regions is necessary for successful spheroid infiltration and that intermediate chemotaxis coefficients provide the smallest spheroid radii at the end of the treatment. We report on the impact of the killing rate on final spheroid composition, and highlight the emergence of spheroid size oscillations due to competing interactions between bacteria and tumor cells.