After reading about the rifle on Bergara's site, probably not the stock with that chassis. I see this kind of stringing all the time with sporter rifles, even though I don't shoot big bore stuff. I would guess it is barrel harmonics; most believe it is only vertical but it is really more of a spiral because of the torque of the bullet being spun up by the twist of the lands. A tuner can help, but most often a little more or less charge will reduce erratic muzzle twitch, for lack of a better term. Think of it like a small shudder that is inconsistent rather than a consistent flex.