In bacterial cells, bidirectional replication of the circular chromosome is initiated from a single origin (oriC) and terminates in an antipodal terminus region such that movement of the pair of replication forks is largely codirectional with transcription. The terminus region is flanked by discrete Ter sequences that act as polar, or direction-dependent, arrest sites for fork progression. Alternative oriC-independent modes of replication initiation are possible, one of which is constitutive stable DNA replication (cSDR) from transcription-associated RNA-DNA hybrids or R-loops. Here, I discuss the distinctive attributes of fork progression and termination associated with different modes of bacterial replication initiation. Two hypothetical models are proposed: that head-on collisions between pairs of replication forks, which are a feature of replication termination in all kingdoms of life, provoke bilateral fork reversal reactions; and that cSDR is characterized by existence of distinct subpopulations in bacterial cultures and a widespread distribution of origins in the genome, each with a small firing potential. Since R-loops are known to exist in eukaryotic cells and to inflict genome damage in G1 phase, it is possible that cSDR-like events promote aberrant replication initiation even in eukaryotes.