The three-dimensional swimming tracks of motile microorganisms can be used to identify their species, which holds promise for the rapid identification of bacterial pathogens. The tracks also provide detailed information on the cells' responses to external stimuli such as chemical gradients and physical objects. Digital holographic microscopy (DHM) is a well-established, but computationally intensive method for obtaining three-dimensional cell tracks from video microscopy data. We demonstrate that a common neural network (NN) accelerates the analysis of holographic data by an order of magnitude, enabling its use on single-board computers and in real time. We establish a heuristic relationship between the distance of a cell from the focal plane and the size of the bounding box assigned to it by the NN, allowing us to rapidly localise cells in three dimensions as they swim. This technique opens the possibility of providing real-time feedback in experiments, for example by monitoring and adapting the supply of nutrients to a microbial bioreactor in response to changes in the swimming phenotype of microbes, or for rapid identification of bacterial pathogens in drinking water or clinical samples.