Most budgie owners have gone through a biting phase with their bird. This phase usually occurs when the bird has bonded fairly well to its owner and has decided that it wants to become the dominant bird. This phase must be dealt with thoroughly. Otherwise, you will end up with a biting little devil on your hands. One sign that your bird is trying to dominate you is if the bird lunges at your finger and bites hard, or just enough to hint that he/she could bite hard when you attempt to move the bird into or out of its cage. If the bird is starting to boss you, and is deciding IF he/she FEELS LIKE going into his/her cage instead of automatically going into it, you have got a dominant bird on the brink of a biting phase on your hands. No matter what, the bird needs to be made to understand that you are, and always will be, the boss. To do this, the owner now has to start bossing the bird. There are various ways of doing so, but what I found worked the best was gently nabbing the budgie and carefully holding him without squeezing in your hand at arm's length for 40 seconds, or until the bird stops squirming around or trying to bite your hand. I will try to explain the proper way to "nab" a budgie, but it is always best if you get a pet store worker who knows a lot about birds to show you how. With this technique, the bird is held in such a way that the head is between the index and middle fingers, while the ring finger, little finger, and thumb hold the rest of the bird against the palm of your hand. The bird's back should be against your palm. The bird should be nabbed when he/she lunges forward to bite or does actually bite.
A biting phase lasts about 2-3 months, until the bird realizes that you are the boss. During this time, you must be sure not to give the bird an inch. As soon as the bird tries to bite, he/she must face the consequences.
Birds will also bite if they feel threatened, jealous, or if their territory has been invaded. Usually, most birds bite only when scared. In that case, it's a matter of earning the bird's trust with continued patience and kindness.
The biting phase with your budgie may seem very tiring and you might begin to feel like you aren't getting anywhere, but if you follow through with the technique described, you'll eventually end up with a kind, curious, bird who respects you.