When you have him out the best relationship you can have with your bird is the relationship of Teacher/Student/ not mother/child.
Have some things that you might want to teach him. Recall training (useful if he ever gets outside and flies away), fetching/ retrieving, turning around on command, waving, shaking hands, having a towel over him, getting him to go on his back etc etc
Or if you have a pretty advanced bird, learning colours, numbers, shapes. But the first bunch should be pretty easy to teach with some dedication and quality time spent.
Greys and other parrots really like to be stimulated in this teaching way and you and the bird will gain a lot more from it than him just simply being out of his cage.