Good advice above. I have a bird exactly like you described. He was almost a year old, in a pet store and just scared out of hit wits at everything. I think he had a bad experience with another person who bought him and then returned him after a month.
It took at least a month for him to get even remotely comfortable. He literally was like a statue everytime I was around, but I could peek through the door crack while he was by himself and he would fluff and preen and sing a little.
I just tried to let him chill, move really slow, mimic the sounds he made and whistle to him, give him millet etc. I did clip his wings, he was a very erratic flyer when I did try to take him out and it was dangerous for him.
With Tobie, he has made a lot of progress but it's relative to how he was before. He does not care to sit with me or on me, he still gets spooked. He did end up with a girlfriend so it may have made a difference if it was only me interacting with him but honestly I don't feel that's the case. It was only because of her coming outside the cage and playing with me or sitting by the window that he will come out to be with her. I slowly got him better at flying by just letting his wings come in but it was and still is really stressful sometimes if he gets scared outside the cage, he still ends up in places he should not be or very erratic but mostly he has learned where to land and enjoys making circles around the room.
I still call him a perch potato. Most importantly he is happy. He likes to sing loudly in the morning and he plays with his toys sometimes. He likes baths, and flying, and I have a boing I hang by the window I let him and Lilly sit there and they will go between the boing and their cage top to eat. After about an hour they put themselves back in the cage LOL ....Or they get into Jasper's cage. I call it their vacation.
Anyway, just to give you some idea what maybe to expect worst case scenario. I've had him for a couple years now at least, I say worst case because of all the scaredy non tame birds on the forum I would say he is still the least people comfortable but I imagine you will have success. The most important thing to remember is everybirdy is different and above all they need love, and a good home, good diet, toys and mostly just to be free to be themselves. We have wants for how they will be, but we don't always get what we "want". Not all Parrotlets talk, not all cuddle, some play more and some less. Some like hands and some don't. Some step on fingers, some step on palms. Some bite, well......ok most bite...
..... Tobie is about the only parrotlet I've ever heard of that won't bite me ever unless I have to hold him by force (when it's unavoidable)
Best advice is never grab her. Keep her safe and go slow, and accept who she is regardless of what you want her to be.