I used to fit my 3-piece Hoyt hunt master and a hand full of arrows into a Camelbak mule when I biked to the range - (I just removed the fluid pouch thingy) - it worked pretty well for a back quiver too.
I've done a lot of Mtn Biking and I have never had good luck mounting anything (that I planned to remove later that day) directly to the bike.
However, if you must go that rout there is a rack that mounts to the seat post and you can get several different and very nice (read expensive) nylon bags made to fit there ...
Also in California they make a kit to mount surfboards on bikes, (think side car) if you cant take your rig apart :p