Don't ship a handgun. That is not legal to do without shipping it to an FFL in the state you are traveling to. USPS will not ship it, you would have to use Fed Ex or UPS and they will require the FFL of the reciever.
Long guns you can ship to anyone as long as the label says it is being shipped to you in care of your friend. I ship rifles a lot and I just label them to Jeremy Cotton, in care of John Doe with his address. Handguns are a different ball of wax.
I would pack both the side arm and the bow. Handguns are easy to fly with. Unload the weapon, put it in a locked pistol size hardcase, put that in you luggage, lock the luggage, declare it at the counter, wait a few extra minutes at the security checkpoint, and that is about it. Take an extra set of locks in case TSA decides to cut yours off. Do not use TSA locks when traveling with firearms, use locks only you have a key to.
There was a thread on here earlier about flying with a bow. Many were using a rolling duffel with a frame. Others, like me, were using a hard bow case. There was some concern about extra bag fees related to the bow cases being larger than airline regulation. Might search for that.
Or go to an archery store and get the packaging for a bow from them. Pack yours in that and ship it. If you ship in a hard case, it will be salty.
Jeremy