Thanks for the additional details, it helps a lot. The display you're seeing happens under different circumstances and you're absolutely right about it possibly being a message that she isn't in the mood for interaction at the moment. Making herself look bigger (fluffing up) and opening her beak to at least 'pretend' to lash out or fake bite is saying "I'm a huge bird and I'm dangerous, I bite, so back up and back off" Of course you know she's a little sweetheart to you and she probably won't hurt you, but you'd be showing her respect and consideration for her own choices if you just let her be for a moment.
Another reason behind this same display is to show a mate or potential mate how beautiful, healthy and symmetrical she is. With birds, symmetry (being the same on one side of their body as they are on the other) is desirable in making similarly gorgeous babies. The open beak may be to invite "beaking" - wherein two birds seem to be biting each other beak to beak, but in the bird world this is our version of kissing; and it often leads to regurgitating to each other which shows what a good provider they are or will be.
So when you see your girl doing this display, decide what it means by her mood.
If she's actually a female you'll want to discourage her seeing you as a mate because she could start egg laying. They will, of course, be infertile, but it can deplete calcium stores in her body and lead to health problems. So try not to pet below the mid back area and don't be touching or tugging at her beak .
You can also encourage her to accept others by being the one to put her on someone elses arm while praising her with big, loud enthusiasm and praise. When we 'throw a parade' for a bird's positive behaviors it reinforces it much more than a simple 'good girl'. In the bird world everything big, loud and impressive makes an imprint
You have a wonderful companion here. Enjoy her and love her for life!