Dear Imran,

No, mutations are not necessarily related to bacterial aging. They are random and may or may not influence aging.

By the way, a single bacterium would probably not age a such. Prokaryotes (what all bacteria are) divide rather quickly, i. e. before they actually show aging.

What actually can age are populations of bacteria. And there, in function of the type of bacteria and where they live, you can have big differences. Because of the periodic division of the single bacteria, populations of bacteria double after a few minutes (or several times in a day or every day ....). So, one counts in "population doublings" or "generations" not in aging of single bacteria.

The lifespan of a population of bacteria depends on external constraints (temperature, space, nutrients, environmental attacks, waste, pollution,  chemicals, radiations, etc. etc. including predators like bacteriophages) which can have an effect on reduction or inhibition of DNA replication, and on internal features (organization, e.g. SOS-response genes to prevent inhibition of DNA replication, formation of exoskeleton-like spores etc.). Mutations can also play a role, which is positive if they enforce bacterial resistance, negative if they badly influence DNA replication etc....

The lifespan in vivo will then last from a few weeks to hundreds of years (if not more, nobody knows !), depending on the type of bacteria (as having been fitted by natural selection) and on their life conditions. For instance, studies done on the survival of some type of E. coli in various soil types have indicated survival times of at least 10 to 25 weeks. While populations of  anthrax bacteria with spores can live up to several hundreds years.

Usually aging of bacterial populations show 3 stages (after a first adaption to the environment) : (1) growth (power law ?), (2) steady state and (3) exhaustion (stop of DNA replication).

The in vitro case can be different. For instance, there is a long lasting study started by Richard Lenski and co-workers in 1988 on 12 identical populations of E-coli. Since February 1988, these populations are allowed to double and followed to track possible evolutionary features. In April 2014, the number of generations amounted 60,000 (at a pace of 6-7 generations/day) allowing for many mutations. Just follow the two links below : to a Wikipedia article and to the RG profile of R. Lenski.

So, instead of a few weeks as in vivo these populations of E-coli have already lasted more than 27 years and will probably continue to live a long more time as there appears to be no sign of inhibition of DNA replication (on the contrary, it seems !).    

https://en.wikipedia.org/wiki/E._coli_long-term_evolution_experiment

https://www.researchgate.net/profile/Richard_Lenski/publications

To be complete, I should add that bacteria have the ability to go "dormant" for extended periods (e.g. in unfriendly environment). So, the lifespan of populations of bacteria can be extended by such periods.