Has anyone considered:
It's two viruses in a symbiotic relationship?
Virus A: Something like an anaerobic rabies that "activates" on death as the oxygen content of the body lowers due to decomposition.
Virus/Bacteria B: And then another flu-like virus/bacteria that can be passed on by saliva to blood (IE you can drink your own saliva and be fine because the virus is too large to be absorbed into your blood stream via your intestines but not too large to be "injected" when you break someone's kin with a bite).
This one kills with a bite, and then the rabies takes over upon death causing you to become someone who bites a lot. Perhaps this is a decomposer bacteria rather than a virus and causes your body to become an anaerobic environment more quickly, further assisting the rabies.
This would also make a hell of a lot of sense from the "genetically engineered virus" point of view that's usually the cause of zombie outbreaks. It might be that only one of the two viruses was intentionally created without people knowing the other existed and thus not knowing they would work together so well, which explains how they could be so stupid as to let this out into the world.
Everyone has Virus A
Somehow Bacteria B gets let out into the world (or the natural bacteria of human mouths mutates).
A few people get bitten, they die of Bacteria B, which decomposes their corpse more aggressively,m making their internal systems an anaerobic environment, activating Virus A, they become the undead and bite others.
Or maybe Bacteria B has been knocking about fairly harmlessly somewhere in Europe and all of America is infected with Virus A. The moment someone from Europe visits the USA and bites someone, they become infected with Bacteria B, they die, they decompose internally a bit more quickly than expected, anaerobic environment is established, rabies activates and they are now a zombie that carries both diseases, few people get bitten by "mad man who was declared dead". some of them travel around etc and it goes world wide.