it would be best if your sister were to join the forum herself if she can to learn about correct budgie care herself, rather than through you.
You're really answered the question yourself. You've noted that your sister's budgie is not happy and biting her. This is completely counter productive if she is trying to bond with the budgie.
You should encourage her to join the forum and to look at the taming and bonding section, where she'll find the answers she needs.
I'm going to close this thread now.