The appropriate answer seems to be that bacteria help somewhat sometimes, maybe.
The evidence for this appears to be mixed, and appears to have been historically controversial.
One old-ish paper claims that bacteria (and more importantly, Archaea) are necessary at least under some conditions. Another somewhat later paper including some of the same authors claims to have found conditions for abiotic dolomite synthesis in the laboratory.
It appears that in terms of mechanisms, the relevant process may involve the proper state of magnesium ions, to which apparently microbes contribute via extracellular polysaccharides:
Literature values for carboxyl group density are not available for all bacteria involved in dolomite formation, however Braissant et al. (2007) demonstrated disordered dolomite phases forming in the presence of the EPS of sulfate reducing bacteria with a carboxyl group density of ~10-3 moles g-1, similar to our values. We suggest that these carboxyl groups promote desolvation of the Mg ion, known to be a kinetic inhibitor in dolomite precipitation (Wright and Wacey, 2004), but are needed in a high density for nucleation to commence.
However, what process exactly is generating geological dolomites appears to be still a matter of debate, and also here, with some suggestive evidence in favor of microbes affecting that process.