The operative part of the quote is "Bacteria can mutate," which is shorthand for the idea that living things can change. The point is both that the original disease that killed so many and made the rest "vampires" is changing, and so are the infected people changing, as the bacteria and its hosts (humans) adapt to one another. (Note also that Neville is changing too, with the knowledge he has just received.)
You need to consider this in the context of what has just gone before. Neville made a slide of Ruth's blood and discovered that she was infected:
"Yes, but—" He broke off as he slid the glass slide onto the microscope.
"Robert, what could you do?"
She slid off the stool as he bent over the microscope.
"Robert, don't look!" she begged suddenly, her voice pleading.
But he'd already seen.
At which point she attacks him, since she's afraid of what he will do to her. (Up to this point Neville has killed every infected person he's found.) When he wakes up, Ruth is gone and he finds her letter.
The letter tells him that the infected have learned to live without always needing fresh blood. They have stopped preying on one another, and the living infected are wiping out the undead infected; in fact the living infected are forming a new society.
What you don't understand yet is that we're going to stay alive. We've found a way to do that and we're going to set up society again slowly but surely.
Neville then simply picks up the microscope:
Then he looked up. Slowly he slid off the stool and placed the microscope back on its base.
He doesn't prepare a new slide, he's still just looking at Ruth's blood. And what he sees simply confirms what he saw before she hit him - she's fully infected. That realization means that a fully infected person can be a person; can laugh, care, and be fully human. (It also means that some of the infected he's been executing were people; that he has been murdering people.)
What Neville had never foreseen, and what nobody else seems to have realized yet, is that diseases and hosts can reach a biological accommodation that allows both to survive. What "Ruth and her people" don't know is that they are not a new people starting their society; they are just human people, slightly changed, trying to put society back together. Bacteria can mutate.