There is Several Options offered here. Just need to know the overall Length the Box Needs to be so when you do start looking you find the one that will work. You also might want to add some Bubble Wrap to give added Protection. When I was shipping Bows the Cost were Much les than Today's Prices. I shipped a 48 inch Compound and was maybe 20.00 Bow they have a sizing scale they use to Take into Account most anything over 30 Inches is considered Over Sized and tacks on a Lot to the Cost. Just realize this as TYD could be a lot more that you Think.
Hope you find the One that Works.
LFM