Definitely don't leave the bird alone in the shower. You don't have to get in with it and the shower can be brief. But then he will have to spend an hour drying off and preening and might be less clingy.
I can definitely see though what is normally a "screaming" problem in caged or clipped birds is becoming a "clinginess" problem in flighted ones. They can fly after you so they don't have to scream for your attention. Yet still they don't want you to go or want to go with you. It's perfectly natural though that the bird wants to stay with you so this is a tough situation to deal with.
One more thing you can try is to have a second person in the room (as a training session) and have them feed lots of rewards to your bird when you leave the room. Naturally you cannot train this yourself because if you're not there, it can't get treats. You can start with the other person holding the bird and holding its feet so it could not fly to you. Moment you leave the room, bird gets treat. Eventually the person shouldn't have to hold the feet. And soon enough the person should be able to stand anywhere in the room, you leave, person walks over to give bird treat. The initial training as you is quite simple. Sustaining this behavior on the other hand is a whole other story.