A senegal could live for 30 years. Three weeks isn't a long time!
Jayde, my new conure (3 yrs old), wanted to spend time with me when I first got her but was also insecure and afraid, so she too would rush to the back of the cage. I often just left the cage door open when I was home and allowed her to go in and out as she pleased. I even wheeled the cage around the house so she could be "with" me without having to be on me.
One day while sitting next to her cage, she climbed down to investigate me. After climbing up and down the sides of her cage she finally ventured onto my shoulder. From there, I placed a perch on the outside of her cage that she could climb onto so she could be closer to me and if she wanted to, she could climb to my shoulder. She didn't like hands or arms and would bite to draw blood or at least inflict a lot of pain! So only way to remove her from her cage was to offer my shoulder.
It was over 3 months of having her before she got comfortable enough to step up onto hands and arms. At first, she was unsure and hesitant, but as her confidence level increased, she became more willing to use my hands and arms as a method to get to my shoulder. She's now been with me for 4 months.
Through all of this, I tried to avoid getting bitten. I'd rather not teach her that I wont listen to her, therefore she must resort to biting to try and communicate with me. If she understands she doesn't have to bite and I wont force her to do something she doesn't want to, then there is no reason for her to bite.