Microalgal cultures are often maintained in xenic conditions, i.e., with associated bacteria, and many studies indicate that these communities both are complex and have significant impacts on the physiology of the target photoautotroph. Here, we investigated the structure and stability of microbiomes associated with a diverse sampling of 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 from which and time at which a culture was initially collected had a stronger impact on microbiome structure than the diatom species; however, some bacterial taxa 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. IMPORTANCE Natural microbial communities are extremely complex, with many more species coexisting in the same place than there are different resources to support them. Understanding the forces that allow this high level of diversity has been a central focus of ecological and evolutionary theory for many decades. Here, we used stock cultures of diatoms, which were maintained for years in continuous growth alongside populations of bacteria, as proxies for natural communities. We show that the bacterial communities remained relatively stable for years, and there is evidence that ecological forces worked to stabilize coexistence instead of favoring competition and exclusion. We also show evidence that, despite some important regional differences in bacterial communities, there was a globally present core microbiome potentially selected for in these diatom cultures. Understanding interactions between bacteria and diatoms is important both for basic ecological science and for practical science, such as industrial biofuel production.