RE: bolt action
Man,
You ask tough questions, Can you give me a situation with a shotgun? There is only one or two bolt action sotguns that I know of, and they are not common. Marlin is the one that comes to mind, but seems there was a 410 or two.
In general what makes a gun accurate is doing EVERYTHING exactly the same every time. More moving parts make this harder, more pieces fitting together increase tolerances, etc.