Always use plain water to bathe your bird. There are several shampoos marketed for parrots, but I recommend that you check with your vet as to the safety of these products before use. The majority of stains on feathers will disappear within a week. If your bird accidently gets into something that can't be removed with plain water, then call your vet to get recommendations as to which products will safely remove the substance. Larger birds and dust producing species of birds will benefit from bathing in the shower.
Several companies market parrot perches designed to be used in the shower.
Make sure the shower perch is grooved to allow a sure footing. Wet PVC can be slippery causing difficulty in perching. Some birds prefer standing on your shoulder for their shower. They can then walk down your arm and assume various positions under the spray. Wearing a tee shirt in the shower will give the bird a better footing and also save your skin.