I once had a guy bring in a macaw who hated bathing the other year.
We tried everything, baths, misting, rubbing him with wet hands, he didnt want to know. Furthest we got with him at first was rubbing him with wet hands or plume spray on fingers, but one evening he was out on the patio in his cage enjoying the evening sun, and I was watering the garden with the hose.
Next thing I know he's fluffing himself up like he wants a bath, so I rained the hose over him and he was loving it.
Odd way to find out but it works.
Each bird is different, and each bird prefers certain times of day for baths also, usually early morning or late evening in the sun.
Personally I'd get him used to a bath. Then just trickle the shower head or tap & sit on the toilet and read a book, act totally blase when he freaks out. He'll soon get bored and curious and go see what the water is all about. This works with most birds I've had in afraid of baths, the mistake made is often the owner making a fuss of the bird when it acts scared and immediately taking it away, or taking the offending object away. Which, in the birds eye, is like saying "Okay, I'll take you away when you play up about it."
A birds nature is naturally quite skittish and scared, but as soon as they realise something feels good, they plunge on in.
My budgie never liked being scratched for ages, he thought my hand was this terrible thing. I kept putting my hand up to him and touching his head until he stopped flipping out about it. Then, suddenly, it was like the clouds parted and this ray of light came down in his mind, and he threw his head to the side like "Yeah... left a bit, mum?"
Same with the running tap. He didn't want to know for ages so I just left him on the kitchen sink one morning and I come in 10 minutes later and he's flinging himself around in it. Sometimes all they need is to realise it's no biggie, and that you're not going to react to them when they throw a tantrum about it.