I use a piece of PVC pipe for longbows. Strap it to the rear passenger foot peg and sissy bar and good to go. My takedowns, I put in a Safari Tuff case and strap across my seat to the sissy bar. I put the arrows in with the bow on the takedown. Duct tape a separate smaller piece of PVC pipe to the larger one for arrows when I'm carrying a longbow. They would fit inside the larger pipe with the longbow, but the arrows don't get mashed around as much in the smaller pipe, IMO.
Now, if your wife is riding shotgun, it probably means you have a fiberglass compartment behind her seat. Should be able to strap a take down case to that fairly easily.