The problem with proofreading
The simplest way to inhibit mutation is to insert error-checking mechanisms. Real organisms use these to make genetic damage less likely - but there is a significant problem with relying on these.
Any proofreading mechanism can fail. You can reduce the chances of these failures by increasing the number of error-checkers - but the more strict they are, the more they will inhibit the reproduction and survival of the organism itself.
If a bacterium has a mechanism that will cause it to self-destruct (or even become less efficient) if it detects even a small bit of corruption, it strongly benefits the bacterium to get rid of the error-detector itself. Which means that strains which mutate out your constraints will dominate, and you'll be right back where you started.
In nature, there is a fine balance between checking and repairing DNA damage that will inhibit the proper functioning of a cell, and being so strict that it reduces the efficiency of the cell. Multicellular organisms are usually more strict and may include self-destruct mechanisms as well - but this is because these mechanisms protect the entire organism from cancer, so there is strong selection pressure in their favor. For a free-living bacterium, self-destruct mechanisms are pretty much always detrimental and will be selected against.
But you don't really need to stop evolution entirely, do you?
Really, the only problem you have is the issue of the bacterium deleting the kill switch. So what you are really looking for is a mechanism to make the kill switch itself something beneficial (when it's not "activated") - and something that will become less beneficial if it mutates. That way, evolution will work in your favor - strains that delete or modify the kill switch will be intrinsically less fit (NOT due to an internal self-destruct switch) and weeded out by natural selection.
The question is, how?
Yes, bacteria can be social. In fact, most of them are to some degree - conjugation, quorum sensing, and the formation of biofilms (colonies of bacteria, often involving multiple specialized roles) all involve chemical communication between bacteria. The ability to exchange information about one's surroundings, cluster into groups, and exchange resources is as beneficial for microorganisms as it is for us.
If you want to make sure the kill switch doesn't change, make the kill switch part of this chemical "language". Any bacterium that alters its switch will be unable to "understand" the information from its peers and will be unable to cooperate with them.
If you want to be really fun, you can even program the bacteria to recognize cells containing the switch as "allies" and make them hostile to organisms that are missing the switch. This will allow them to defend themselves against rival species (and their host's immune system) in addition to actively killing off their own mutant strains.
The kill mechanism itself is simply a toxin that mimics the chemical the bacterium uses to communicate. Metaphorically speaking, it's a "killing word" and the only defense is for the bacterium to be "deaf" - which will make it less functional.
As a bonus, if the ability to cluster into biofilms is a significant part of what makes the disease dangerous to humans (it often is), even if a strain becomes solitary and eludes the switch, it will be significantly less dangerous and therefore no longer a problem.