Swarming bacteria move on agar surfaces in groups, using flagella as motive organelles. Motility depends critically on surface wetness, which is enabled by osmotic agents and surfactants secreted by the bacteria. In a recent study, the upper surface of an Escherichia coli swarm was found to be stationary, as determined from the motion of MgO particles deposited on the swarm. This led to the remarkable conclusion that the bacteria move between two stationary surfaces - the agar gel below and the liquid/air interface above. That study suggested that secreted surfactants may contribute to immobilizing the upper surface of a swarm. Here, we test this proposition using two robust surfactant-producing bacteria. We find antithetically that the upper surfaces of both these swarms are mobile, showing a superdiffusive behavior in swarms with stronger surfactant activity. Superdiffusive behavior was not observed on the surface of a drop of bacterial culture, on bacteria-free culture supernatant, or on nonswarming surfactant-producer colonies, which suggests that superdiffusion is an emergent property resulting from the interaction of the collective motion of the bacteria within the swarm with the surfactant layer above. Swarming not only allows bacteria to forage for food, but also confers protective advantages against antimicrobial agents. Our results are therefore relevant to superdiffusive strategies in biological foraging and survival.