Bacterial cellulose biofilms are complex networks of strong interwoven nanofibers that control transport and protect bacterial colonies in the film. The design of diverse applications of these bacterial cellulose films also relies on understanding and controlling transport through the fiber mesh, and transport simulations of the films are most accurate when guided by experimental characterization of the structures and the resultant diffusion inside. Diffusion through such films is a function of their key microstructural length scales, determining how molecules, as well as particles and microorganisms, permeate them. We use microscopy to study the unique bacterial cellulose film via its pore structure and quantify the mobility dynamics of various sizes of tracer particles and macromolecules. Mobility is hindered within the films, as confinement and local movement strongly depend on the void size relative to diffusing tracers. The biofilms have a naturally periodic structure of alternating dense and porous layers of nanofiber mesh, and we tune the magnitude of the spacing via fermentation conditions. Micron-sized particles can diffuse through the porous layers but cannot penetrate the dense layers. Tracer mobility in the porous layers is isotropic, indicating a largely random pore structure there. Molecular diffusion through the whole film is only slightly reduced by the structural tortuosity. Knowledge of transport variations within bacterial cellulose networks can be used to guide the design of symbiotic cultures in these structures and enhance their use in applications like biomedical implants, wound dressings, lab-grown meat, clothing textiles, and sensors.