I think you should be fine introducing him to having baths now. I would suggest putting a large dish of water in his cage to see if he will bathe himself but many people do take showers with their birds using a shower stand, which might be more of an option for you.
Hope this helps.
As long as the baby is fully weaned and fully feathered, baths should start ASAP. Once a week is the minimum amount a bird needs to be bathed, but many enjoy doing it more often (especially when it's summer and hot out!). You can either offer him a shallow pan of lukewarm water to see if he'd like to bathe himself OR try spritzing him with a fine mist of water. If you spritz him, be sure you buy a brand new dedicated spray bottle for the bird and never use it for anything but pure, clean water!
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Ditto above, of course try slowly and gently with him and find what he enjoys the most. Be it a dive in a shallow dish, a fine misting, running under a tap or going whole hog and hoping in the shower. The last thing you want is to frighten them with a bath. Make it a game/play time
Birds and baths. They need 'em. They love 'em, but on their terms. Parrots can take baths in so many different ways, and usually have their one favorite way.
1. Shallow sturdy dish of neutral color either in the cage or on table
2. Misting the parrot while perching on a chair back, gently misting from behind, never directly into the face. If he don't like that, try a misting bottle with a different color tip. Salts likes one with a blue tip, a red tip gets him very scared . Try spraying UP, and letting the mist fall down on him naturally.
3. Sinks - some parrots LOVE sink baths, with the warm water dribbling out of the faucet. Some like it with more the a dribble.
4. Sopping wet Kale or other broad leaf veggie, left on top of the cage - some birds like to roll around on the leaves, wetting themselves and having a snack at the same time.
5. Taking a shower with you on a sturdy shower stand, either the suction cup kind or you can make one for about 10 bucks with PVC piping and some epoxy from your local DIY shop. Just be careful for too hot for the water and watch the soap splashing off you and onto your parrot. Some Amazons go absolutely crazy for this, as do some macaws.
6. Any combination of the above. Salty likes his mist bath, a shower bath once in a while, but always, always finishes off by taking a bath in his water bowl in his cage - way too small for him, in a corner so he cant get more then his head in, but there you go.
Experiment a bit, you'll find the method your parrot likes the best , when you hit on it, they will let you know, throwing the head around, extending their wings, even getting vocal sometimes.
I pat Salty semi-dry with a neutral color towel, lightly patting the big wet drops off, and then set him u in his cage with a space heater aimed at him from like 10 feet away
My IRN, Rain, loves when I put a few ice chips in water. Rain will reach in for them and before you know it begins fluffing up, sticking his head in and out of the water and splashing it all around.