The physical properties of collectively swimming bacteria have been thoroughly investigated both experimentally and theoretically using simulations. While models successfully predict some aspects of the dynamics observed in experiments, both models and experiments vary in their underlying assumptions and physical conditions. Hence, it is not clear which models are appropriate for which experimental setups. Here, we study, both experimentally and using two types of models (agent-based and continuous), the statistics of two strains of Serratia marcescens, wild-type and a nontumbling strain, swimming on a two-dimensional monolayer at varying concentrations. The experimental setup allows for a direct comparison with simulation results. Both models capture some aspects of the dynamics but fail at displaying others, especially at high densities. In particular, the effect of tumbling is much more significant than mere rotational (angular) diffusion.