I can go into Merlin's cage to take him out, but he gets rather offended when I rotate his toys or clean the cage, so generally Husband takes him to the Man Room when the cage cleaning is going on - otherwise I can't do a great job.
We also have to move our Caique to their playstand while his cage is being cleaned - he just would rather be dirty and tries to take the sponge away angrily otherwise!
I've been lucky in that he has only bitten hard enough to draw blood twice - in almost 12 years - but I also took him home at 6 weeks of age, and know his body & eye language.
I taught him from the get go that he was never allowed on my shoulder - Husband will attempt to put him there sometimes (as he lets Merlin on his), but Merlin just WON'T as he's been conditioned it's not okay to be there. I like my eyes/ears/lips/cheeks...you know, facial features.
One of my friends has a Grey who won't let anyone else but family pick him up - I'm the only non-family member who has had the patience and understanding to take the time to get to know Dakota from afar in order to pick up his queues - and can hold him & spend quality time with him. Even though I don't see my friend & Dakota often (we live 600km apart now), he does remember me when I visit.
Over time, you'll learn how to read each other, and come to a more natural understanding and appreciation for each other It just takes time, and a lot of observing.