Get this battery case:
Mojo Refuel Armor S Battery Case for iPhone 5/5S| ibattz : Global Removable Power Leader
It allows you to interchange the battery in the battery case with i9300 batteries for Samung Galaxy phones - they're cheap, compact and light. Each add on battery gives you the same charge plus a bit that is in the iPhone battery. With the display off, the iPhone running an app like Cyclemeter would use about 10-15% of the battery per hour.
Get this from QuadLock case to mount the above on your stem. You just take the "universal mount" thingie and stick it on the back of the case above. Then the whole thing mounts nicely on your stem.
Quad Lock ? Bike Kit - Universal Fit
J.