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Bacteria have evolved a vast diversity of functions and behaviours which are currently incompletely understood and poorly predicted from DNA sequence alone. To understand the syntax of bacterial evolution and discover genome-to-phenotype relationships, we curated over 1.3 million genomes spanning bacterial phylogenetic space, representing each as an ordered sequence of proteins which collectively were used to train a transformer-based, contextualised protein language model, Bacformer . By pretraining the model to learn genome-wide evolutionary patterns, Bacformer captures the compositional and positional relationships of proteins and can accurately: predict protein-protein interactions, operon structure (which we validated experimentally), and protein function; infer phenotypic traits and identify likely causal genes; and design template synthethic genomes with desired properties. Thus, Bacformer represents a new foundation model for bacterial genomics that provide biological insights and a framework for prediction, inference, and generative tasks.