Hi Cassie,
I adopted a budgie about 6 months ago. She came to me from a family that had 2 cats and these cats wanted her badly. So they kept her in the cage and hung it high up near the ceiling so that the cats couldn't get at her. She was never let out of her cage and they really didn't interact with her much at all for almost 2 years that they had her. So when I adopted her needless to say she was terrified and wouldn't come to me at all and if I tried to coach her out she would just latch onto my finger with a bite and did not want to let go. (That sure hurt my finger and my feelings) But, I brought her for a checkup and a clipping (Haircut and manicure). Then I started giving her lots of attention and talking to her to ease her nerves, I would get her in my hands and hold her gently snuggled against me for about 20 minutes or so at a time. After about 2 months of that she now wants to be with me. She comes right onto my finger and will do a step-up from one hand to the other. It just took a lot patience, she still a little hesitate to come right to me at times but I just keep my hand just on the edge of her cage door talking to her and she then will in time come to me. I do take her away from her cage so that she can't see it and will spend quite a bit of time with me.
So it can be done, but first get the flight feathers trimmed(Haircut)so your little budgie can't fly from you and just hold him/her gently snuggled to you so that he/she will see that you can be trusted and that you won't hurt her/him. In time your little budgie will see it's okay to come out and trust you.
Good luck
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