There are 3 bomb bags to obtain and 1 capacity upgrade that affects all 3 bags.

Effect - Code

Bomb Bag 1 - Purchase from Barnes Bomb Shop in Kakariko after 2nd temple.
Bomb Bag 2 - Free the goron from the giant lava rock located underwater in zoras domain.
Bomb Bag 3 - Destroy the rock barriers for the River Canoe mini-game owner.
Bomb Bag Capacity Upgrade - Score 25 points or more on the River Canoe Mini-Game.