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. ### Competing Interest Statement The authors have declared no competing interest. Wellcome Trust, 226602/Z/22/Z LifeArc, IH001 Ineos (United Kingdom), Oxbridge AMR Doctoral training programme NIHR Cambridge Biomedical Research Centre Cambridge Centre for AI in Medicine (CCAIM) doctoral training programme Swiss National Science Foundation, TMSGI2_226252/1, IC00I0_23192 Peter und Traudl Engelhorn Foundation Engineering and Physical Sciences Research Council, EP/T022159/1 Science and Technology Facilities Council, DiRAC