The natural oil in the feathers reduces the dirt sticking so most of it should just come off with the wash. Can't use a brush, it will damage the feathers. You will struggle with the room in buckets. Ours go in the bath and then get a shower rinse. When you have got the worst off, her natural daily preening should do the rest.
Before blow drying sponge off the water with a towel. Be careful not to rub the feathers as they will break. Just stroke the water through and out of her feathers. Be careful of the heat when drying or you will burn her skin and feathers -must be cool setting.