The majority of grouse I've shot in the last 15-20 years have been with either a .22 pistol ,currently a S&W 422 , or more typically an old Benjamin .177 pump pistol, head shots.
It's nice and quiet , no , you can't have it!
I did get a couple this year with the bow and small game heads though.
Being quiet and not spoiling "bigger" plans is key.