It is generally acceptable to break a bow that is lying on the ground. There is no hit requirement for how hard you have to hit a bow to break it, and most people don't want their bow getting swung at full force if they can avoid it. Usually if there is a marshal within hearing range, just lay your sword on the bow and announce that its broken.
Shields are different, since it's up to the wielder to determine if a red hit was good enough. This may vary from realm to realm, but you usually can't just go around breaking shields that are lying on the ground.
you can also check out this thread, as it's come up before:
viewtopic.php?f=3&t=34344