Algal cultures are often maintained in non-axenic conditions, i.e., with associated bacteria, and many studies indicate that these communities are both complex and have significant impacts on the physiology of the focal photoautotroph. Here we investigate the structure and stability of microbiomes associated with diverse diatoms during long-term maintenance in serial batch culture. We found that, counter to our initial expectation, evenness diversity increased with time since cultivation, driven by a decrease in dominance by the most abundant taxa in each culture. We also found that the site/time from which a culture was initially collected had a stronger impact on microbiome structure than the diatom species however, there were some bacterial taxa that were commonly present in most cultures despite having widely geographically separated collection sites. Our results support the conclusion that stochastic initial conditions (i.e., the local microbial community at the collection site) are important for the long-term structure of these microbiomes, but deterministic forces such as negative frequency dependence and natural selection exerted by the diatom are also at work.