Time Between Death And Reanimation:
In the comics, it has never been specified, as far as I can recall; however, it always seems to take at least a couple of minutes, and never more than a few hours.
On the show, Dr. Jenner at the CDC gave us an official answer:
We had reports of it happening in as little as three minutes. The longest we heard of was eight hours. In the case of this patient, it was two hours, one minute, seven seconds.
- S1:E6, "TS-19"
However, Shane reanimated in under two minutes, and in S6:E2, "J.S.S.", we saw at least one person reanimate in a few seconds. It seems likely that reanimation takes however long the scene demands.
Time Between Bite And Death:
AMC has tweeted a list of rules pertaining to zombies on The Walking Dead, which included this tidbit:
Zombie Rule #10: Once you're bitten you'll die and reanimate as a walker. How long it takes is related to the nature of your bite.
The reason that the amount of time between being bitten and dying is contingent upon the nature of the bite is simple: bite kills you via blood loss or normal infection, not because of the zombie virus. Everyone already has the virus, so that isn't fatal.
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.”
- The Walking Dead Wikia, quoting Robert Kirkman's statement in the "Letter Hacks" column of the comic books
As Kirkman's comment makes clear, the zombie virus has nothing to do with the cause of death - if you are bitten and die of infection, the infection that killed you wasn't the zombie virus, it was regular old sepsis or something along those lines, because zombies have filthy mouths.
So you might be bitten in the throat, severing an artery; this will kill you very quickly. We've seen this happen to several people, including Andrea's sister Amy. On the other hand, you might be bitten on the torso, where no major arteries are accessible; in this case, you will die much more slowly. This is how Jim died, and he appears to have lasted almost a day before he finally succumbed to the infection. Likewise, Bob was able to hide his bite and live for more than a day after being bitten. He didn't even appear to show signs of infection until after his lower leg was amputated by the Terminus cannibals.
Along the same lines:
The pathogen itself does not kill its hosts, but it seems to weaken their immune systems considerably, to the point where even minor illnesses are far more fatal than normal to humans.
- The Walking Dead Wikia
"You all know how this shit works. You get a bite, you get any kind of wound from these things, something from them gets in you...and you fucking die."
- The Walking Dead, Issue #122, "All Out War: Part II"