why do the bites speed up the death process?

I've wondered that too! They say it's not the bite that kills you but that you get infected when you are bitten, even though everyone is infected already, so everyone will change over when they die, no matter what. But then if your arm is bitten and you cut it off, you're ok..... Ahh!! So confusing. 🙃

It's the acute infection of the bite: pathogens release toxins into the bloodstream, causing acute septicemia.
Yes, they are all infected, but with it at a non-lethal state, sort of like "herpes" in the body. It lays low until and unless you are stressed , sick, sunburn etc.

Definitely a good question. How does a bite accelerate anything at all? Is there some sort of venom in the teeth that spews out into the victims bloodstream when the tooth contacts human flesh? Not all undead have tongues, so I doubt it's that. How does the infection transfer faster after being bitten?

Still no answers on how bites accelerate the infection, what exactly happens when a walker tooth penetrates a victims flesh?

The fanboy answer is usually either that the bite wound itself kills you (moronic) or everyone is so seriously ill (virtually on the brink of death) that the bite puts you in immediate danger of getting the flu like symptoms that lead to death.

They're both idiotic. There must be something in the mouths of the walkers.

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We all have inside us the type of bacteria that consumes dead organic matter. It remains dormant until we get an injury that causes localized tissue death, or of course when it all dies. The mystery agent seems to do the same thing. It's present in every living person but dormant until they die. Then it goes active, restarting the most primitive parts of the brain, slowing down normal decomposition, and so forth. When a walker bites someone I think the active variant is injected into their blood stream - but it doesn't go back to sleep. Its activity is harmful to the living body and poisons the bite victim as it reproduces and spreads. That's my personal theory.

You have to view it as two separate issues.

A bite causes an infection that kills you, nothing more. It doesn't change you into a walker. It just kills you probably because no one had time to create a cure or antibiotics are not available.

Once you die (and you don't have to die by a bite) something in the brain reanimates and gets the body up and moving (rewatch season 1, episode 6 when they are at the CDC). It has nothing to do with a bite...which is why "everyone is already infected".

I'm "assuming" that a bite enters the bloodstream, where being splattered with guts and gore doesn't.....when things get too confusing I just remind myself that "it's a show based off a comic about the dead walking....it's entertainment don't think too much." (LOL)