If you're bathing the bird just because, don't. My birds get extremely stressed when I've had to bathe them in the past. Too much washing can also remove all the good coatings from the feathers and degrade them.
Generally, no need to wash them. But, if you needed to for a reason then you need low/no scent, AND low sudsing. I have had success with an all natural “dish soap” for baby bottles and it is sold at Walmart. I tested 3-4 types of soaps that were liquid, non scented, and mild. It was important to me that it rinse out easily and quickly. They do not really like baths…however all chickens I have bathed love the hair dryer. Yes, you will need to dry their fluffy undercoat bc they will get too cold if you don’t, as it doesn’t dry very quickly on its own.