I' d definitely leave the the bolt in the gun. There' s no problem checking a rifle as long as you declare it and it' s in a locked case. The Airlines don' t care if the gun is operative or not as long as you declare that there is no ammo in it. Most times when I fly with my rifles they don' t even open the case at the check in desk. they have me open just enough to slide in the firearms declaration tag.
You' d probably have a tough time explaining what the hunk of metal in your carry on was at the Security Checkpoint. I got stopped for a pair of finger nail clippers a while back. They gave me 2 options, go check them in and stand in the 45 min line again, or throw them away.......somebody got some free nail clippers!!