This paper presents a systematic analysis of the motion of microscale structures actuated by flagellated bacteria. We perform the study both experimentally and theoretically. We use a blotting procedure to attach flagellated bacteria to a buoyancy-neutral plate called a microbarge. The motion of the plate depends on the distribution of the cells on the plate and the stimuli from the environment. We construct a stochastic mathematical model for the system, based on the assumption that the behavior of each bacterium is random and independent of that of its neighbors. The main finding of the paper is that the motion of the barge plus bacteria system is a function of a very small set of parameters. This reduced-dimensional model can be easily estimated using experimental data. We show that the simulation results obtained from the model show an excellent match with the experimentally-observed motion of the barge.