How can I carry my compound bow in a backpack without showing any parts of it?
There are a couple of good answers suggesting alternatives, and a comment or two about hazards, of these choices.
But you can purchase a TV Moving Box, online or from the local moving company and truck rental place. They are designed for flat screen TV's These are available in different sizes starting at about $25. Put your bow in it and carry it like it is a flat screen TV.
Alternately: you can purchase a takedown bow that would be easier to pack, but I don't think that is what you are looking for.
Alternately: You can get an Army Duffle Bag, with shoulder straps, it is effectively a large backpack. It should hold your bow, arrows and other gear, while functioning as backpack. Amazon sells them new for about $50 with several surplus stores selling used ones for about $20