If your budgie is becoming increasingly aggressive and biting, it's likely because it's still wary of you and hasn't established trust. Spending more time with your budgie and increasing your interactions can help. As it gets familiar with you and develops a sense of dependence, it's less likely to be aggressive.

Reasons for Increased Aggression in Budgies and Solutions
Budgies, especially females, are naturally wary birds. While they may be affectionate when young, they can become less friendly and even aggressive as they mature. Hand-raised budgies tend to be more approachable than cage-raised ones, due to their consistent interaction with humans, and are less likely to bite. Cage-raised budgies, even with daily interaction, spend more time in their cage, leading to a lack of closeness with their owners. Reduced daily contact can exacerbate this issue. To counteract this, owners should spend quality time with their budgies, focusing on building a bond. This will encourage them to be more affectionate and strengthen your relationship. If your budgie is already aggressive, you can implement training methods to correct this behavior.
How to Tame a Budgie
Taming a budgie requires patience. Start by communicating in a soft tone to help it relax. Then, slowly introduce your hand into the cage, gently holding the bird until it stops moving erratically. Avoid abrupt grabbing motions; instead, allow it to get used to your hand. Once calm, move your finger in front of its face. Take your budgie to another room and, if needed, trim its wings to prevent escape. Repeat the process of gently handling it and releasing it multiple times to encourage relaxation and habituation, and then return it to its cage, speaking to it calmly. With consistent effort and a patient approach, you can successfully tame your budgie and improve its temperament. Consistent interaction, gentleness, and patience are key to achieving a friendly and well-adjusted pet bird.