Bacterial colonization of cancer tumors is widespread. While the clinical significance of intratumor bacteria is widely investigated, the dynamics of tumor colonization remain underexplored. We monitored bacterial population dynamics in murine tumors after introducing genetically barcoded Escherichia coli cells by intravenous or intratumor injections. Barcode sequencing from resected tumors after intravenous injection suggested that narrow bottlenecks dominate infection and are followed by rapid, yet highly nonuniform growth. Within a day, bacteria reached a steady state and subsequently sustained load and clone diversity. Results from intratumor injections, circumventing the infection bottleneck, revealed that sizes of bacterial progenies followed a scale-free distribution matching Zipf's law. Theory suggested that our observations are compatible with a growth model constrained by a local niche load, competition for a global resource, and noise. Our work provides the first dynamical model of tumor colonization and suggests that descriptive statistics may allow distinguishing genuine tumor microbiomes from contamination.