Four inch groups are disappointing, but if everything else checks out, I concur, try bedding it. Before you go that route though, it might be worth playing around with barrel shims to see if a change in the pressure point helps or hurts.
Having said that the scope is new, I assume it is also untried. You might want to try a proven scope on that thing to ensure it is indeed a rifle problem.
If you handload, 41 grs of H-4895 with any good 180 gr game bullet should produce good to excellent accuracy in a .308.