In condensed matter physics, simplified descriptions are obtained by coarse-graining the features of a system at a certain characteristic length, defined as the typical length beyond which some properties are no longer correlated. From a physics standpoint, in vitro DNA has thus a characteristic length of 300 base pairs (bp), the Kuhn length of the molecule beyond which correlations in its orientations are typically lost. From a biology standpoint, in vivo DNA has a characteristic length of 1000 bp, the typical length of genes. Since bacteria live in very different physico-chemical conditions and since their genomes lack translational invariance, whether larger, universal characteristic lengths exist is a non-trivial question. Here, we examine this problem by leveraging the large number of fully sequenced genomes available in public databases. By analyzing GC content correlations and the evolutionary conservation of gene contexts (synteny) in hundreds of bacterial chromosomes, we conclude that a fundamental characteristic length around 10-20 kb can be defined. This characteristic length reflects elementary structures involved in the coordination of gene expression, which are present all along the genome of nearly all bacteria. Technically, reaching this conclusion required us to implement methods that are insensitive to the presence of large idiosyncratic genomic features, which may co-exist along these fundamental universal structures.