I would consider that the root or main bone. One way to check is to scale the bone, rotate it and change it’s location in pose mode. If the rest of the rig works at any scale, location or rotation, you have a good working root bone. Just resize the bow, place it in your scene and key that bone on the first frame of your action. Done deal. If it does not work, at any scale location or rotation, some tweaks to the constraints or parenting may be needed.
If you could upload a blend with your armature, I could take a look. I don’t need the mesh items. Having the string available might help. Some proxy meshes as stand ins for your bow model would help too, but not necessary.
You should never have to change your rigs in object mode. A proper root bone and a rig designed with the root bone in mind makes any object mode manipulation pointless. Just change the location, rotation and scale of the root bone in pose mode and begin your animation.
I have a tutorial planned explaining the root bone and it’s uses in one of my Rigify tutorials. Unfortunately, it’s not complete yet. I’ll try to get it done and uploaded to show it’s proper use. I consider it the most important bone in any rig.
If no one here chimes in, there are some good people in the CgCookie community forums that have a lot of experience and knowledge about Blender to Unity workflows.
Edit: Since your post count is not over ten, you are under moderation and cannot upload files to this site. A prefered site to upload is pasteall.org. There is a tab for blends. Upload your file there and post the link here.