The last comment, not really true. I managed to beat the cave of ordeals with only a few arrows, and not a single bomb. I only used two fairies, nothing else. Of course it can be helpful, but not necessary. There's also a cheat for unlimited bombs and arrows, if you really want to beat it that bad, although it spoils the fun of the combat.
http://www.youtube.com/watch?v=O3sPnJcV6jQ It can be helpful, as bomb arrows kill most enemies in one hit, except armoured ones which fully block the attack. And, about the bridge, like the others said, it belongs to the bridge of eldin, which is to west on the wii version.