Welcome to the forum,
What makes you say the bird is depressed? Is she not eating, plucking, pacing etc?
Does this bird get out of the cage at all?
Making a relationship with this bird will be a little harder for you because she is bonded to your sibling.
Do you both live with your parents/in the same house? Where does the bird live?
If you live in your own houses, then ask if your sibling will relinquish the bird into your care, and take the bird to your house.
If you both live in the same house, and the birds cage is in their bedroom, move the birds cage into your bedroom. If the bird lives in the living room, you can leave it be if that is the place you spend the most of your time.
Start off by making sure the bird is getting a balanced diet. If you read a few threads here in the forum you will see we all have different diets for our birds, but none are seed only. They must include veg - not iceberg lettuce, but dark greens are good, broccoli, green beans, peas.
Plenty of food info here:
Feathered Food Court | Avian Avenue Parrot Forum
Next you need to be patient and consistent in interacting with the bird.
You need to be interacting with her every day.
Start by spending time around the cage, talking to her, offer her a treat through the bars (I like to use sunflower seeds,in moderation, and millet) if she spooks, back off - try again later.
She should start accepting the treat pretty quickly, especially if you choose something she is fond of.
Next is out of cage time, if you are in your bedroom, close the door and open her cage door. Just sit on a chair or on your bed and let her come out in her own time, I like to read when doing this (if your bird is peach faced, dont read a paper book, use an electronic device). It´s important not to sit and stare.
When I found Aldora I did this with her every day, she was quite bitey, I would keep an eye on her using my peripheral vision, and if she landed on my shoulder, I would look at her with my head turned at an angle (so my nose wasn´t pointing at her).
Let the bird come to you, eventually she will. Keep treats close by, and give her one when she comes close by. I would break an inch chunk off a millet spring and place it on me. So, on my head, shoulder or knee, Aldora would come over and munch away and I´d talk to her - yes, it got very messy!
Don´t worry about getting the bird back in the cage, you will find it easy enough if you have let her out for enought time. Don´t do this when you have to leave the house in half an hour etc. You will stress trying to return her to the cage and it may hinder progress.
I can´t tell you how long it will take for her to be comfortable coming and landing on you, but with patience you will get there in the end.
RE biting, my advice to you is this: don´t take it personally. Don´t let it get you down or think the bird doesn´t like you. Birds aren´t like that.
I find that the bite is for a reason. You need to figure out what makes her bite and avoid those things. Obviously there are some that are unavoidable. I´ll give you some examples,
Aldora bites if I have no shoes/socks on and she sees my toes wiggling. She attacks thinking it is a predator/threat. Solution: wear shoes when she is out of her cage.
Aldora bites if you approach to stroke her. Again, she thinks she is under threat and attacks. Solution: I don´t pet her or go near her with my fingers.
She bites when I go near her cage. That´s her home, she´s protecting it. Solution: I never put my fingers in her cage (my boyfriend does and she does notbite him, she likes him more.) I still offer her treats through the bars.
But even with all of this, she still gets let out of her cage everyday so she can stretch her wings. I have let her out every day since the day I found her, I had an issue once getting herback in the cage, but I just left her and eventually she returned of her own accord.
I haven´t been bitten in a long time, not that she wouldn´t, she´s a fierce bird. If she gets spooked she will not only stand her ground, she will launch the attack and rip chunks out of us. We are still working on our relationship and hopefully in the future it will be even better.
If the bird would land on your siblings hand, you may find it easier than me and Aldora to build trust.
There´s no set method that is a one pot wonder. All we can give you are pointers, or share our experiences.
Don´t worry about ¨Am I doing it right¨, as there really is no right way.
As long as you avoid the obvious bad things, no sudden movements, or outbursts (eg. screaming GOAL at the top of your lungs watching sports), not ramming your fingers in her cage ect.
Speaking of cage, if she is in a small cage, maybe you could upgrade it. It is important to have a good size cage as it ill affect their happiness. Minimun is 18x18 (A good size cage is at least 30 across so that they can have short flight).
I´m sorry for the frequent use of the word ¨bird¨, you didn´t mention her name.
Good luck, I hope you are able to build a great relationship and give her a loving home and a fullfilled life