Our 4-H group recommended Dawn dish washing liquid - the original blue one, which has blueing (sp?) to make those feathers really sparkle. Assuming, you know, you get some feathers, it might matter...
It kills some nasty smells, too.
The first time we bathed a bird, it was our WCBP rooster, who was filthy after a muddy week of dipping his head feathers to eat and drink. We were practicing for eventual show entry. Well, he relaxed so much into the shallow bath water, I swear, we thought we'd killed him. The kids were freaking out, screaming at me that we'd killed him, and he was just SLEEPING. In the tub. With me holding his head out of the water. Didn't rouse till we were rinsing him withe the shower sprayer hose, and even then, we had to support him. He finally perked up with a nice towel rub, and I breathed a sigh of relief. Till I turned on the blow dryer, and he slowly collapsed again.
It was that very moment when the kids decided they would never, ever want to show a bird at the 4-H fair.
In retrospect, it was a pretty funny experience, but at the time, it was terrifying.
The only other bird we ever bathed was our crevecoeur hen, who went through the same deep relaxation routine. At least this time, we knew she'd survive. No more bird baths for us.