Conures are pair bond birds, and they tend to overbond if they are not handled by more than one person.
What you have is a bird that is tame, that was never properly socialized.
You need to start from scratch with this bird, and train it from the basic taming and no bite, through step up.
It will probably take about 1-4 months before the bird fully trusts you...
He isn't mean, when you look at it from the bird's perspective,
You are basically overriding this bird's survival instincts by handling it. In the wild, you would never get close enough to touch, let alone, pick one up.
By letting you do that, this bird is quite literally trusting you with it's life. Think about what that entails...
So the first order of business is to earn this bird's trust.
Then add the dynamic that this bird is bonded to it's person, and that person is gone. It's in a new place, with strangers, and probably disoriented.
So, he becomes defensive, and bite-y. That's the dynamic here.
When the bird knows it is safe and can trust you, it will relax. Then you need to socialize it around strangers.