I've been trying different ways to haul my 1pc longbows on my bike and I think I've finally found a method that works great, at least on my bike.
I ride all year round and stop at the range most days right from the job. I got a Molle Shotgun Scabbard off the auction site. They run $30 to $35 or so. They come with metal D-Rings and a sling, which I remove, and are well padded. We've been having some ugly weather lately and my baby is dirty, but she's getting a bath and polishing this Tuesday!
I picked-up a couple carabiners at Home depot and some zip-ties.
One carabiner goes up top on the backrest frame. I leave this one loose so I can move it around to adjust for different bags I carry.
The other one goes down on the upper frame tube, this keeps the scabbard high enough that it is against the hard parts of the bike when bungied down so the padding is protecting the bow.
This is what the scabbard looks like. I'm thinking about attaching one of my molle mag pouches to it to carry accessories, armguard etc...
Here's how she rides with just my arrow tube.
This is loaded with my gear and Maxpedition Jumbo EDC bag I carry most all the time. I'll have no trouble hauling my hunting gear with this set-up.
I can easily just slide the bow out or simply un-clip the scabbard and carry the bow with it on. Nothing is in the way while riding, the bow is well protected. This is the simplest rig I have come up with and am very happy with how it works. I was about to sell my Shelton since I couldn't shoot it on a regular basis due to the hassle of hauling it. She'll be staying with me now!