Many bacteria secrete extracellular polymeric substances that promote surface adhesion, biofilm formation, and nutrient entrapment and retention. Here, we report a new physical mechanism by which polymeric substances modulate the collective motion of motile microorganisms. We experimentally investigate the dynamics of swarming Serratia marcescens in quasi two-dimensional (2D) liquid films and demonstrate that even minute amounts of polymers (≤ 100 ppm) can significantly affect the structure and dynamics of bacterial swarms. The presence of polymers, whether added or naturally occurring, promotes large-scale coherent structures and suppresses velocity fluctuations; velocity distributions change from super-Gaussian (without polymers) to Gaussian (with polymers). Spatial and temporal correlation functions show that added polymers increase the length scales of flow structures, whereas the flow time scales are governed primarily by the average swarming speed. Interfacial microrheology data indicate that both the added and bacteria-secreted polymers enhance the solidlike (elastic) properties of the film interface. Combining these observations with the kinetic energy spectra analysis, we propose that swarming bacteria in thin films generate propulsion by applying forces to the (visco-)elastic film surface that propagate into the bulk. Our findings reveal a mechanical role for bacterial exopolymers beyond their traditional structural roles, whereby polymer-mediated interfacial elasticity facilitates coordinated propulsion and modulates the spatial and temporal scales of the emergent collective order in bacterial swarms.