Well, here I am again. Weird thing happened : I had to clean the whole bottom of the cage today, making lots of noise and movement. Naturally, the poor bird got scared, but this had to be done. That's not the weird part though; the weird thing was that after the whole ordeal, my budgie became more floofed and calm than before. This event helped her relax than any sweet talk or distance I gave her prior to this (of course, I talked to her during the whole thing to calm her). Anyone had experience like this before?
The fact that she saw you go through the entire process with the noise and movement and realized you weren't trying to grab or hurt her helped her recognize she isn't in the danger she perceived herself to be in previously.
This is a good sign her trust in you will begin to increase over time.