I use tide with bleach alternative on my white birds. Works wonders!
Put 1/4 cup of tide in 1 gallon of warm water.( I put a little less in so I can scrub stains with the rest) Splash around/stir the mixture until it becomes sudsy. Place bird in the water and grab an old tooth brush or something similar. Dip the toothbrush in the tide leftover from the 1/4 cup. Scrub the bird with it, going in the direction of the feathers.Make sure to get the soiled areas extra soapy. Let the bird sit, body submerged, in the water for five minutes. Now, rinse the bird with white vinegar (I dump a little in and add more if I feel I need to) to make sure you get all the soap out. Then, rinse the bird for the last time in plain water.
I sometimes use Mr. Clean Magic Erasers on their legs or any stains before I wash the bird.
( DONT let the bird drink the water
DONT let the bird dunk its head under the water
DONT get the soap on the birds face
DONT get the birds ears wet