It has taken my brother a few months to "tame" Petra, his female Eclectus. She bit a lot when he first got her and he was about the only person she liked. Now she is a diff bird even with me. There are still times when she won't step up and will try to bite. That will likely always be the case with any bird.
I have had Harley, my male Eclectus for right at a month (he came home May 14). That is still a work in progress and yes there are days we seem to go backwards. Be patient and consistent and always include bite pressure training. Maybe have her step up on a thick stick or dowel rod. You'll get bit much less often and can keep building trust. I am a new parront myself, but your girl sounds a bit like my boy and I am just sharing what is working for me. And that is far from perfect, it is overall positive progress from when he first came home.
So let me make sure I have the bite pressure training correct...when my finger is in her mouth, I tell her "good girl." When it becomes too much, I tell her "gentle." Today, when she bit, I told her "no," and gave her a timeout in the cage. (Problem is she likes her cage and the issue is getting her out.)
I tried the dowel rod and it worked once. Ever since then, she runs and then bites it immediately. I'm just going to have to try several things and see what works for her I guess.
Hopefully the experienced people will chime in

I'd recommend that you check out the advice I was given on thread I started on this forum seeking biting advise lol. Some great tips in there. There is also a sticky post on bite pressure training on the Training forum with some great advice by Anansi.
I am no expert, so I can only share my limited experience with Harley and Petra. For me, at first I would make him step up on a stick when he was biting to make me go away. I felt this was important to do in order to show him he can't bite me to get his way, and what he wanted was to be left alone. This is why time outs didn't work on him and likely won't for a long while. They DO work on my galah, but he is way more social.
When I had him step up on the stick, I kept him in the cage at first then gradually brought him just outside of the cage door. When he stepped up on the stick I would tell him good boy and talk to him softly while feeding him treats. Now, sometimes, when he was really pissy, he would walk to the end of the stick I was holding and try to bite me. When he would try, I would distract him with a treat to make him pick his head up, and would say "Good boy, no Bite". I would only have him perch on the stick for a few minutes before I put him back on his perch in his cage where he felt safe. My goal was to show him 1) nothing bad will happen when he steps up for me and 2) that good things happen when he does (and doesn't bite). Distracting a biting beak with a treat works well too btw

Anyway, I did this every day before work and every day after work for a few weeks in the beginning. I eventually stopped using the stick and did the same exercise using my hand, wrist and forearm. I haven't had to use the stick for stepping up in a while.
On the actual bite pressure training, when he is perched on me, I tell him good boy when he doesn't bite down hard. When he does bite down and starts to increase his pressure to where it starts to hurt, I will gently grab his top beak between my thumb and finger, say "No, no bite" and remove his beak from my skin. After a while he got the hint when I say "no bite" and reach for his beak.
Whatever method you chose to train her not to bite, you have to be consistent and patient, and learn their body language of when they are trying to bite you hard vs. not.
Harley stepped up on my hand very easy tonight. I have it on video. I'll try to post it when I figure out how. Just keep working with her and keep in mind that a week (especially the first week home) isn't enough time to expect any drastic improvement. It will take several weeks to months, but you will see it if you are consistent and patient
