Flagellated bacteria can swim across moist surfaces within a thin layer of fluid, a means for surface colonization known as swarming. This fluid spreads with the swarm, but how it does so is unclear. We used micron-sized air bubbles to study the motion of this fluid within swarms of Escherichia coli. The bubbles moved diffusively, with drift. Bubbles starting at the swarm edge drifted inward for the first 5 s and then moved outward. Bubbles starting 30 μm from the swarm edge moved inward for the first 20 s, wandered around in place for the next 40 s, and then moved outward. Bubbles starting at 200 or 300 μm from the edge moved outward or wandered around in place, respectively. So the general trend was inward near the outer edge of the swarm and outward farther inside, with flows converging on a region about 100 μm from the swarm edge. We measured cellular metabolic activities with cells expressing a short-lived GFP and cell densities with cells labeled with a membrane fluorescent dye. The fluorescence plots were similar, with peaks about 80 μm from the swarm edge and slopes that mimicked the particle drift rates. These plots suggest that net fluid flow is driven by cell growth. Fluid depth is largest in the multilayered region between approximately 30 and 200 μm from the swarm edge, where fluid agitation is more vigorous. This water reservoir travels with the swarm, fueling its spreading. Intercellular communication is not required; cells need only grow.