Well, Commodore, that's very well expressed. In fact, McCoy was asked to leave the bridge on two occasions (usually under stress but delivering a nicely comedic effect)... When Commodore Decker in Doomsday says indelicately "You may leave the bridge, Doctor." And the other occasion is when Spock is telling McCoy to go back to sickbay to work on his Therigan derivative.
"Please leave that to me, Dr. McCoy. I realize that the crew are your prime concern. You can best serve them in your laboratory. I urge you to confine yourself to it until a remedy has been found."
I can't ever recall Kirk asking McCoy to leave the bridge, can you?
Also remember, Kirk was McCoy's best buddy. When Bones wasn't busy, he was hanging out because Kirk let him. Kirk didn't exactly run the tightest ship in the fleet, how many episodes ended with everyone falling around laughing? A lot of the time, Bones is palling around. I'm sure if there was something vital going on in Sick Bay, he'd be down taking care of it. Otherwise, he's a bit of a slacker. In Conscience of the King, he's more concerned with tying one on than listening to the XO voice concerns about the captain.