The Handi is problematic getting the best accuracy off the bench, because of the way that the forend connects to the barrel. Lots of us put an 0-ring over the stud to float the barrel and that seems to tighten groups somewhat. When benching the rifle, be sure to maintain the same contact spot on the front bag. My trick is to slide the rifle forward until the front bag contacts the trigger guard. This puts the contact point at about the hinge and seems to help in load development. Once the load is developed, get away from the bench and shoot the rifle as usual.
PawPaw gives excellent info above, I owned 2 Handi-rifles and must say honestly did not like them, while overall quality was fair accuracy was not up to standards for me. Personnaly if it's a money issue I would look for a used bolt or buy one of the new low cost Ruger rifles.