I would think Batman was the quieter one, and he probably gave the impression of ignoring Robin's chatter. But the second he stopped Bruce was all...what's the matter? Why aren't you nattering on?
Like the story of the wife who complained for years that her husbands snoring kept her awake, but after he died, found the silence was "louder" than the snoring.
It's like in that one story where he says Robin's puns are music to his ears.:-)
I think he said that after Robin had nearly died one time, so the kid still being able to breath was saving him a whole lot of paperwork and having to hold audtions, so yeah, he'd be happy. But after a week or so he'd be back to hoping the next villain DOES gag the little chatterbox.