In The Walking Dead, Season 3 episode 16 (Welcome to the Tombs) Milton is stabbed to death by the Governer then left in the same room Andrea is being held in to reanimate and kill Andrea. He hadn't bit anyone else, and he seemed like a pretty clean guy, so why did Andrea die? She didn't die of the initial bite. She also didn't seem to be suffering from blood loss. What was the cause of death, infection, or something else...?
There is a bigger back story I think you've missed. In S1-Ep6:
It is revealed By Dr. Edwin Jenner That EVERYONE is infected! No matter how you die, you will become a zombie, period!
Then, in the episode you are asking about, though Andrea was bitten, that was not the cause of death:
Andrea didn't die from being bitten, She is found just after being bitten and killing the Milton zombie. She asks to kill herself and Rick gives her his gun. Michonne stays in the room with Andrea while she does the deed.