To pull back the bow string you have to be looking at a block within your render distance, then you can look up and fire. Gets really annoying in combat.
MCPE-5592
Bow firing bug / annoyance
Resolved
Fixed
0
(Unassigned)
Unconfirmed
Tablet - iOS - iPod Touch
bow, distance, firing, rendering
0.7.6
0.8.0
Retrieved
This appears to have been resolved in version 0.8.x for iOS