There's a moment of surprise as the arrow hits his neck and Bruce has just enough time to think what in the...? an arrow??? before everything goes black on him. Good thing Cap was there to catch him, he nearly starting falling in the direction of the drop off the building. He had a vague feeling of being carried but once they're in the jet, he's down for the count, limp in Cap's arms as he's put onto a bed.
At least it wasn't the Hulk they had right now. Bruce would be out for most of this trip back to the mansion.