Whew - A muddy Brahma is a BIG dirtball! Mine, except for Herman and the two Kindergarten Dropouts, are all under two pounds. None really get full baths more than once or twice a year, a day or two before a show.
You need three tubs of water (Rubbermaid type bins work well) and a small bucket - The first tub is warmish soapy water - usually Dawn or a mild livestock soap we use for the show calves. The second two are cooler, clean rinse water. The middle one will sometimes have a bit of vinegar in it to cut any soap residue remaining.
We usually tag team it - one person holds and gently rubs in (and out) the soap, the other scoops water and runs interference for potential escapees. We don't do a heavy-duty "wash behind your ears" sort of bath, it's more just to get out the loose dirt and encourage them to thoroughly preen, which straightens out and oils every feather, not just their usual spot-grooming. Herman is the exception. He's fluffy enough (and dirty enough) that he actually gets "swished" back and forth to make sure he's thoroughly wet.
After the bath, we wrap the "bathee" in a towel. Show birds will get a quick blow dry (on cool) just to make sure all the feathers are laying in the right direction. Herman gets a full blow dry. Holy Cow, he's poofy, then ... and he's a true Sulking Silkie for the rest of the afternoon!
I don't know how that system will adapt for your Brahma, but it works for our midgets, so that's how we do it. We've got the advantage of having smaller birds who are all used to (if not particularly happy about) getting baths. And luckily, I have NO white chickens!
PS - If you DO decide to bathe your mudpuppy, take some pictures. It's liable to be very entertaining ... for everyone but your hen!
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