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Bacteria colonize environments that contain networks of moving fluids, including digestive pathways, blood vasculature in animals, and the xylem and phloem networks in plants. In these flow networks, bacteria form distinct biofilm structures that have an important role in pathogenesis. The physical mechanisms that determine the spatial organization of bacteria in flow are not understood. Here, we show that the bacterium P. aeruginosa colonizes flow networks using a cyclical process that consists of surface attachment, upstream movement, detachment, movement with the bulk flow, and surface reattachment. This process, which we have termed dynamic switching, distributes bacterial subpopulations upstream and downstream in flow through two phases: movement on surfaces and cellular movement via the bulk. The model equations that describe dynamic switching are identical to those that describe dynamic instability, a process that enables microtubules in eukaryotic cells to search space efficiently to capture chromosomes. Our results show that dynamic switching enables bacteria to explore flow networks efficiently, which maximizes dispersal and colonization and establishes the organizational structure of biofilms. A number of eukaryotic and mammalian cells also exhibit movement in two phases in flow, which suggests that dynamic switching is a modality that enables efficient dispersal for a broad range of cell types.