My birds like to join me in the shower but they do Not want any actual droplets to hit them.
I only bring them in if I'm gonna take a long hot soaking shower. What they Love is the steam-humidity in the room. At first I only brought Sunny in, but I when I realized how much she loved to relax in the hot steam, I brought the semi-tame budgies as well, and they clearly love it as well.
To bring the budgies into the shower, I have to first "trap" them inside their own cage - by waiting till they're inside and closing the door - and then either roll their big cage from the front of house to back - or else reach in, catch them in my hands to put in smaller cage to carry back to bathroom.
In the past, any time I did such a thing, they would avoid being "trappable" for days, exiting their big cage when I came near. Also determinedly avoid my hand if I would reach in.
However, since starting occasionally bringing the budgies to join me for a steam-shower, they have done the Opposite! Hanging around INside their big cage when I come near. For the most recent shower, LETting me take them in my hand with barely a token avoidance-hop. Jefferson even once has flown to the back of the house to check whether I might be running a shower...
Once I actually complete my shower, they are NOT interested in exiting the bathroom. They will sit in there for hours if I let them, even after the steam has visibly dispersed. And they just seem to love it.
So. I hope they are never injured by this, since they seem to love it so much. I am always as careful as I can be. Part of the reason I don't shower with them as often as they would probably like, is the safety measures I feel compelled to take before bringing them in there, such as covering inaccessible areas, trying to put away any dangers I can perceive, etc. I probably don't need to bother, since the budgies just want to spend the time sitting on the tension rod over the tub. (It's an extra shower curtain, installed OVER the tub, to use for hang-drying of clothing items. Only, now it's my birdeis' shower perch.)