Well I have 8 big parrots, 16 cockatiels, 35 parakeets, a heap of finches and canaries. I have had birds for 30 years.
Here are my questions for you. Any idea on age? What kind of parrot is it? What were the living circumstances (neglected, abused, ignored)? Is it in a cage or ON it's cage? Do you know if it was ever hand trained? Was the previous owner male or female? Is the bird male or female. What food are you feeding?
If you want it to trust you go buy some vanilla wafers. Walk in the room and place half a cookie between you - slowly eat the other half in front of her saying mmmmm and yummy. My birds will KILL for vanilla wafers. Only give the bird one when YOU go near it. No one else. It won't take long for her to figure it out. Then she will come towards you as soon as she sees one in your hand. Then you can go from there.
Just so you know - I have a wild caught 30 year old moluccan cockatoo who has never tamed down and is terrified of hands. I have had him 8 years. I have reconciled that he will always be afraid and we deal with it. I also have a yellow nape amazon that is the most vicious thing alive. I respect his space and he lets me feed him (I have to grab the dishes quick) But I also have an eclectus that is the most lovable critter around. So, it depends on the bird. You should read a parrot psycology book. They have odd ways of thinking. (Like a male bird will bite it's human female if someone comes near to 'protect' her from danger and make her move away)