It is said that when a vampire drinks human blood, its eyes turn red. How come Edward's eyes did not turn red after drinking Bella's blood?
Well, we know that all vamps in the Twilight universe are, by default, red at the time of their transformation from human to vampire. We know that vampires who drink human blood continue to have red eyes. Those who choose to become vegetarians have eyes that eventually change colors and become golden (unless they haven't fed in awhile and then they become black).
However, the change from red to golden isn't immediate the first time a vamp drinks animal blood. I believe this is discussed more in Breaking Dawn. I would imagine the same would be true for a vampire who has been a long-time "vegetarian" and, for one reason or another, ingests human blood. One time drinking human blood doesn't change eye color, but a consistent diet of human blood would.
We know that the Cullen family only eats animal blood which is why they have golden eyes. The reason Bella's eyes are red at first is that even if you don't drink blood immediately your eyes still turn red. After you consistently feed on animal blood your eyes will turn golden. The reason Edward's eyes don't turn red is because he is not consistently eating human blood.