Hi there and
to the forums!
You've been given extremely good advice by FaeryBee and Therm. I'm so glad that Pepper has such an understanding and caring mum
I agree that the best you can do for now is give her lots of time with regards to taming. Spending lots of time in the same room with her, reading, talking to her, etc. is a great way to start to show her that she can trust you.
Be sure to read through the forum's many Budgie Articles and "stickies" (threads "stuck" to the top of each subform for easy reference) to ensure you're up to date on all the best practices for budgie care!
If you have any questions after reading through everything, be sure to ask as we'd love to help
We look forward to seeing you and Pepper around the forums! Good luck