I am not a fan of using dishwashing liquid--I feel it strips oil from their feathers too much. That said, many people who show their chickens do. I generally use baby shampoo, although my very favourite is parrot shampoo. I have used dog and horse shampoo, but generally find no added value to justify the cost when I can get a good sized bottle of baby shampoo for about a dollar. If I am concerned about mites or lice I do use dog flea/tick shampoo.
I sometimes blow dry and sometimes do not--it depends on the temperature, how many birds I am washing and the amount of time I have available. A heat lamp should be available if you don't blow dry, unless putting back into hot outdoors with plenty of time for the bird to dry before it cools off for the night.
After the bath I wrap in a towel for at least 10 minutes to absorb as much of the water as possible. While wrapped up I trim toes nails and beak as needed, clean out any gunk that has collected in the crevases of the comb and oil the comb and toes.
I generally treat with ivermectin pour-on while the feathers are still wet--absorbed into the skin, not feathers.
