Yes Dawn dish soap works really well on birds. Just a couple of drop will do in a dish tub.
Oh also a heating pad with a towel over it works great at keeping them warm after a bath.
Use slightly soapy warm water in a dish tub, place her in slowly, then use your finger to wipe her feathers to clean off the dirt. Then use a hose wand and rinse her off gently. Towel dry, use blow dryer on low setting, till she's completely dry. Hope that helps.