It's not so much the decision that takes him half a second as the phrasing.

"It'll probably be best if you do handle it."

Bruce needs control. He can't give him much right now, but he can let him have control. It rankles, to some degree. Part of the frustration, after all, is his own lack of control. But as long as the lines are clear, as long as he's handing that control to Bruce instead of having it taken away because he's incompetent or insane...