Pathogenic bacteria such as Listeria and Yersinia gain initial entry by binding to host target cells and stimulating their internalization. Bacterial uptake entails successive, increasingly strong associations between receptors on the surface of bacteria and hosts. Even with genetically identical cells grown in the same environment, there are vast differences in the number of bacteria entering any given cell. To gain insight into this variability, we examined uptake dynamics of Escherichia coli engineered to express the invasin surface receptor from Yersinia, which enables uptake via mammalian host xcexb21-integrins. Surprisingly, we found that the uptake probability of a single bacterium follows a simple power-law dependence on the concentration of integrins. Furthermore, the value of a power-law parameter depends on the particular host-bacterium pair but not on bacterial concentration. This power-law captures the complex, variable processes underlying bacterial invasion while also enabling differentiation of cell lines. 