I show white rock bantams, and I have been told not to use any "blue" shampoo because it will stain, either blue or a yellowish tint, unless you get *all* the residues out, so you must be very careful with those.
Ivory dish soap is the one most reccommended, especially if you let the chooks sit in the sun while sudsed up for a couple minutes before rinsing. A rinse with vinegar cuts the soap the best. After bathing, air dry in a cage with lots of shavings and a clean perch overnight.
I have found that wire bottomed cages won't let the firm poops fall through, and my white birds always get dirty from the goo left over from a messy poop falling through the cage bottom. Wire also breaks off feathers if the birds flap (more of a problem with males).
Black feathers have not been much of a problem for me. 6-8 weeks before a show, pull speckled/spotted feathers from the wings or tail and pray they grow back in white. While washing, get any dark ones in the body/hackle you missed before. I have noticed that my birds with a bit more black flecks also have a more vibrant white color, while the birds from a different breeder and less black are a duller white and not as much shine to their plumage.