From my reading on M. tuberculosis, I know that this organism has a pretty high mutation rate
Huh, that's news to me. In fact, Mtb has a rather low mutation rate and rather low genetic variance. See the paper by Sherman & Gagneux in Nature genetics. The paper does state that mutation rate in latent infection is higher than expected or previously assumed, but that's a different story.
That said, mutation rate depends strongly on the genomic context. You can have mutator strains in E. coli or other bacteria that exceed the mutation rates of other strains by orders of magnitude.
A clinical example of a bacterium with mutator strains that help in acquiring resistance is Pseudomonas aeruginosa. More on that in the paper by Ferroni et al..