While bacteria divide clonally, horizontal gene transfer followed by homologous recombination is now recognized as an important and sometimes even dominant contributor to their evolution. However, the details of how the competition between clonal inheritance and recombination shapes genome diversity, population structure, and species stability remains poorly understood. Using a computational model, we find two principal regimes in bacterial evolution and identify two composite parameters that dictate the evolutionary fate of bacterial species. In the divergent regime, characterized by either a low recombination frequency or strict barriers to recombination, cohesion due to recombination is not sufficient to overcome the mutational drift. As a consequence, the divergence between any pair of genomes in the population steadily increases in the course of their evolution. The species as a whole lacks genetic coherence with sexually isolated clonal sub-populations continuously formed and dissolved. In contrast, in the metastable regime, characterized by a high recombination frequency combined with low barriers to recombination, genomes continuously recombine with the rest of the population. The population remains genetically cohesive and stable over time. The transition between these two regimes can be affected by relatively small changes in evolutionary parameters. Using the Multi Locus Sequence Typing (MLST) data we classify a number of well-studied bacterial species to be either the divergent or the metastable type. Generalizations of our framework to include fitness and selection, ecologically structured populations, and horizontal gene transfer of non-homologous regions are discussed.