In microscopy, new super-resolution methods are emerging that produce three-dimensional images at resolutions ten times smaller than that provided by traditional light microscopy. Such technology is enabling the exploration of structure and function in living tissues such as bacterial biofilms that have mysterious interconnections and organization. Unfortunately, the standard tools used in the image analysis community to perform segmentation and other higher-level analyses cannot be applied naively to these data. This paper presents Bact-3D, a 3D method for segmenting super-resolution images of multi-leveled, living bacteria cultured in vitro. The method incorporates a novel initialization approach that exploits the geometry of the bacterial cells as well an iterative local level set evolution that is tailored to the biological application. In experiments where segmentation is used as precursor to cell detection, the Bact-3D matches or improves upon the Dice score and mean-squared error of two existing methods, while yielding a substantial improvement in cell detection accuracy. In addition to providing improvements in performance over the state-of-the-art, this report also characterizes the tradeoff between imaging resolution and segmentation quality.