The Bushnell Banner is their bottom of the line scope. I'd never put it on a rifle with that level of recoil. Do so if you wish. I wouldn't and I like Bushnell scopes but would never consider one below their Trophy line for such use.
Now onto the question. No way the rifle is shooting that low or left IF you are on at 100 yards. Has to be either a shooter problem or a scope problem. If you can go back and shoot the same small group at 100 yards with it then I'd rule out both scope and rifle as the problem. Free floating is not gonna help your 200 yard groups if the rifle is really consistently shooting as you say at 100 yards.
GB