I recommend against bungee cords because they stretch and move around. Also more than about 10 lbs, they're not very good. Instead use something like these OR Accessory Straps: http://www.outdoorresearch.com/site/...ry_straps.html

Tie the backpack down and cinch it down tight, make sure you use both straps and tie off the ends so they don't get caught in the wheel or elsewhere. If you have something rigid you can stick inside that might help, for example a clip board or text book could help stabilize it. I have the 48" straps but I wear my backpack when I ride. I've used the straps to tie all kinds of stuff to my bag that cannot fit inside like a pair of steel toe boots, computer keyboard, flatbed computer scanner, half a box of network cable, etc. Just have to get creative.