Hello there! As I mentioned in my introduction post, I have quite the older female budgie named Alex. She used to have a friend with her in the cage whose name was Robin, but he unfortunately passed away. She's been alone ever since, and although she seems content on her own, I've decided that I want to bond with her so she doesn't have to be alone anymore.
I started this process yesterday, and she already seems okay-ish with my hand outside her cage. I've been showing her my hand, and moving it around the outside for her to look at and get used to, but for some reason she sometimes very suddenly lurches in its direction and makes a small soft chirp noise. I think she's trying to bite it? Other than that, she doesn't run away from it anymore if it's outside her cage and moving slowly, and she ruffles her feathers and closes her eyes when I'm talking to her. I was told that that is a sign that they're relaxed and calm, which is a good thing... until she lurches and tries to bite me lol.
Anyways, I was just wondering if it's possible for a budgie to be territorial of their cage, and if so, how to solve that. And if it's not that, then I think she's seeing my hand as a threat. How do I show her that I mean no harm to her? Or am I doing something that she could be genuinely uncomfortable with? Any help would be much appreciated!
I uploaded a picture of her in the attachments, but it uploaded sideways. No idea why.