No, the moulting shouldn't change anything, although she/he might be a bit grumpy with all the pin feathers and itching that comes with a moult. You could try misting her with a spray of warm water, that helps them. I think you would be better to start off by putting your hand in her cage as I suggested and let her get used to your hand in there first, try getting her to step up onto you whilst in the cage, because when she is out of the cage and on top of your budgies cage, she's no need to step up, she can just fly right back to her cage if she wants to. It took me six months to realise that I have to be in control of my bird and not him in control of me, which is what was happening to me. Dooby ruled the roost totally, he was a demon, he would bite at every given opportunity, because I let him do what he wanted basically. You will have to take charge, be patient and firm, make her step up in the cage, that's the first start, then once she has stepped up, you can take her out and let her fly, then you must get her to step up again to put her back in. I wouldn't let her stay out all day like you have been doing, but that's just my personal choice, my reason is, she is then doing what she wants to do all the time. So, with mine, they come out first thing in the morning, I take them out one at a time, give them a kiss and let them fly, they are out for about an hour flying and playing, then I go and get their breakfast, I put that in their cage and put them back in, usually, they see their breakfast and go in for it anyway. Then after about an hour in the cage, I take them out again for flying and playing. When they are in the cage, it give me time to throw open the windows and have a tidy up etc. etc. that the way I work it with my two. Bedtime is between 6.00p.m. and 7.00p.m. and they get covered up (I leave the bottom half of the cage uncovered) then in the morning, they get uncovered around 7.00a.m. and another day begins. I hope this helps, I know Tike2 will back me up when I say patience is the key word here. I am not the most patient of people, but if I feel I am beginning to lose my patience with them, I leave the room for five minutes, calm down and then start again. You haven't had her for very long, so it's still very new to you both as I said before, you have to learn to trust each other. You will get there, Tike2 never thought she would make progress, but look at her now!! LOL.