While bacterial chromosomes were long thought to be amorphous, recent experiments reveal pronounced organizational features. However, the extent of bacterial chromosome organization remains unclear. Here, we develop a fully data-driven maximum entropy approach to extract the distribution of single-cell chromosome conformations from experimental normalized Hi-C data. We apply this inference to the model organism Caulobacter crescentus. On small genomic scales of 104-105 basepairs, our model reveals a pattern of local chromosome extensions that correlates with transcriptional and DNA loop extrusion activity. On larger genomic scales, we find that chromosome structure is predominantly present along the long cell axis: chromosomal loci not only have well-defined axial positions, they also exhibit long-ranged correlations due interacting large emergent genomic clusters, termed Super Domains. Finally, our model reveals information contained in chromosome structure that can guide cellular processes. Our approach can be generalized to other species, providing a principled way of analyzing spatial chromosome organization.