If I find the exact starting position (say 1152471) of the coding sequence of a given gene in the genome of a bacterium, is the genome of the bacterium in general stable enough so that I can expect to find the same position in a different member of the same species?
Genetic variation within bacterial species can be much higher than one might expect.
First, this can be a difficult question to answer quantitatively because even just testing whether two strains are part of the same bacterial species is difficult: the "gold standard" method is actually experimental and involves whole-genome DNA-DNA hybridization (with a cutoff of 70% relatedness). Modern sequencing approaches have shown this usually corresponds to around 95% average nucleotide identity (ANI) (see here).
However, an ANI of 95% does not actually mean that the genomes are 95% identical: it means that of the shared sequences, one expects 95% of the nucleotides to be the same. The percent of the sequences that are actually shared in the first place can be much, much lower. For example, this paper compared 61 sequenced strains of E. coli. Out of the ~15K genes observed in at least one genome sequence, only 6% of genes were observed in all strains. Variably-present genes made up around 80% of a typical E. coli genome. This is a high level of variability, but not outrageous: an analysis of only nine P. putida genomes, for example, showed a core of at most 33% (ref).
So, if a gene is indeed indeed present in two strains of the same bacterial species, then it is likely to be highly conserved. But there is also little guarantee of finding the exact same set of genes in two strains of the same species. This means you cannot naively take chromosomal coordinates from one strain and apply it to another: you need to actually figure out which sequences correspond to one another in your genomes.
If all your samples are, say, E,coli K12 MG1655, there will be very little difference between the published sequence and what you have. If you have another strain of E.coli, you can't count on there being no indels at all between the two strains.
The locations of a gene on a bacterial chromosome is determined arbitrarily, so you would not expect coding sequences to necessarily have the same numerical values. Remember that the bacteria's transcription machinery will use promoters in the genetic sequence to determine where to start transcription, so the actual start location doesn't really matter -- it's pretty easy for random mutations to add or delete a few base pairs between several genes!
Instead, you would search for the genetic sequence of the gene you were interested in on the genome of a closely related species. Since many genomes are annotated by identifying genes from closely related species, it is possible that two closely related genomes start at exactly the same place, but you should definitely not assume that this will always be the case.