So it's been a while since this thread has posted, but with Alex here, I thought I'd update.
I decided to draw a little warm bath for him, as well. At first, he seemed to have no interest in bathing. He was only drinking out of it, until...

He didn't actually "bathe" in it, so to say. He just got in it as he was drinking. It didn't completely wash out the baby food from his face or chest, but it helped somewhat.
Of course he saw it as drinking water before bathing water. It seems birds can't tell much of a difference.

And of course, Lucy, being the nosey little butt that she is, tries to photobomb. If I took this just a second later, she'd probably have her whole head in.

Lucy started drinking out of it while Alex was in the bath, so I decided to get one for her as well. Aside from a few sips, no one seemed interested.
I do notice that the water bowl gets dirty fairly often though. Maybe he's already trying to bathe. Either that, or Lucy's being a butt and dropping pellets into it for no specific reason (I have seen some whole, uneaten pellets in it).
I will be very glad once he's weaned, so he can get all that baby food off of him. It's been clumped to the feathers next to his beak for the longest time, and is impossible to get out.