In TWD, Sophia's bite did not appear to be such a bleeder that it was the cause of death. It seems the bite turned her into a walker while she was alive (like Jim).
From all three examples, the implication of a bite is that a victim is actually in some mid-state of death, or "zombie-ism," so to speak while technically alive. So, they do not have to die before the disease has altered whatever brain function triggers typical zombie traits.
I can't speak on other productions, but that's not how it works on TWD. In fact, Jim was never even shown as a zombie. They left him by a tree, still alive, & succumbing to the infection
Afterward they witness Jenner's TS-19 data. He states that TS-19 was a person (His wife) who was bitten & agreed to be used for study. He scans to the 1st event where it shows the infection "Invade the brain like meningitis" & cause death.
For 2:01:07 TS19 was dead, & then the reanimation process began, which is a phenomena that happens to everyone in their world, post-mortem.
Exposure to even a superficial bite causes infection, which causes death. Reanimation is caused by death alone. They operate independent of one another, though perhaps not entirely unrelated. Although, since any death results in resurrection, I tend to believe they probably are unrelated