[I'm sure we have a skilled microbiologist somewhere here, so he would correct my answer.]
The necessity to designate gene locations in classical bacterial model species predated the genomic era, so traditional maps were normally neither bound to origin of replication, nor were they necessarily expressed in base-pairs. In E. coli, for example the traditional map was created based on the F-pili-mediated DNA transfer experiments.
When whole genome sequences became available it was only natural to continue the traditionally defined numeration in terms of placing the "base-pair one". Thus, in E. coli "the traditional and physical maps ... linkage map are closely correlated".
My understanding of the current situation with bacteria without genetic prehistory is that their genomes are numerated either respective to classic closely-related species (if any) or according to the presumed location of ori. Just to give an example of how the dilemma was solved for the Buchnera genome: it was "assumed the DnaA box upstream of the gidA gene is the replication origin" and the authors decided to designate "the start of the DnaA box as base pair one".
As you see, still, even if the authors try to define "base-pair one" based on the position of ori, the problem is that this point depends on the ori-searching tool one uses and on the contemporary understanding of how ori-sites look like (direct determination of origins of replications are in many cases not easy). See e.g. this table with a revision of ori locations in a set of genomes: while most of the genomes received their numeration irrespective of ori, some of them were indeed bound to it, but the new analysis showed that these locations were inaccurate.