Robert Kirkman, the creator of the Walking Dead franchise, has explicitly stated that "zombieism" has nothing to do with people dying of zombie bites.
"The rule is WHATEVER it is that causes the zombies, is something everyone already has. If you stub your toe, get an infection and die, you turn into a zombie, UNLESS your brain is damaged. If someone shoots you in the head and you die, you're dead. A zombie bite kills you because of infection, or blood loss, not because of the zombie "virus.""
- Originally written in the "Letter Hacks" section of an issue of the comic books, and quoted from the TWD wiki.
So you can examine deaths related to zombie bites on the show, on a case by case basis, and rule out the ones where the victim obviously died from blood loss or some other traumatic injury. You'll be left with all the cases in which the person died of an infection. According to Kirkman, the infections in question are not related to the zombie "virus", but are more mundane infections that probably have something to do with the obvious filthiness of a zombie's mouth.
This is actually quite plausible, in terms of medical science. Prior to the invention of antibiotics, it was very common for doctors and morticians to die from infections caused by accidentally cutting themselves while performing a dissection or autopsy. Dead bodies are full of all sorts of horrible pathogens, and if you introduce them into your bloodstream, you are going to become very ill very quickly.
Zombies, obviously, eat dead bodies all the time, and their mouths are filled with rotting flesh. Thus, being bitten by a zombie is a great way to get a horrible infection, and for whatever reason, antibiotics don't help at all.