My local FFL complains about having to pay extra for trash service to get rid of all the packing materials. You might ask them if they'll hold a box out for you. Even better, two boxes. Having learned my lesson shipping stuff, a little extra work double-boxing is well worth the effort.
If you use bubble wrap, tape it to the gun, then wind tape tightly around the wrapped gun. A lot of damage comes from the gun moving around inside the box. Use cardboard or hard foam shims or blocks to make sure it can't shift. If it can move, it can wear holes in the sides or punch the barrel out an end. You don't need "shock absorbing" near as much as you do "firmly held."
Also, take pictures of the wrapping and boxing process; if you should have to make a damage claim, the first thing the shipper will say is "it wasn't packaged properly." I've only had to the email pictures to settle a claim once, but it was a $5000 shipment completely destroyed (forklift operator ran the forks through the side of the crate instead of sliding them underneath!) and the freight company folded and wrote me a check.
