In this article we present a computational model for the simulation of self-propelled anisotropic bacteria. To this end we use a self-propelled particle model and augment it with a statistical algorithm for the run-and-tumble motion. We derive an equation for the distribution of reorientations of the bacteria that we use to analyze the statistics of the random walk and that allows us to tune the behavior of our model to the characteristics of an E. coli bacterium. We validate our implementation in terms of a single swimmer and demonstrate that our model is capable of reproducing E. coli's run-and-tumble motion with excellent accuracy.