Cyanobacterial blooms occur in lakes worldwide, producing toxins that pose a serious public health threat. Eutrophication caused by human activities and warmer temperatures both contribute to blooms, but it is still difficult to predict precisely when and where blooms will occur. One reason that prediction is so difficult is that blooms can be caused by different species or genera of cyanobacteria, which may interact with other bacteria and respond to a variety of environmental cues. Here we used a deep 16S amplicon sequencing approach to profile the bacterial community in eutrophic Lake Champlain over time, to characterize the composition and repeatability of cyanobacterial blooms, and to determine the potential for blooms to be predicted based on time-course sequence data. Our analysis, based on 135 samples between 2006 and 2013, spans multiple bloom events. We found that bloom events significantly alter the bacterial community without reducing overall diversity, suggesting that a distinct microbial community -- including non-cyanobacteria -- prospers during the bloom. We also observed that the community changes cyclically over the course of a year, with a repeatable pattern from year to year. This suggests that, in principle, bloom events are predictable. We used probabilistic assemblages of OTUs to characterize the bloom-associated community, and to classify samples into bloom or non-bloom categories, achieving up to 92% classification accuracy (86% after excluding cyanobacterial sequences). Finally, using symbolic regression, we were able to predict the start date of a bloom with 78-92% accuracy (depending on the data used for model training), and found that sequence data was a better predictor than environmental variables.