Bomb Bag - Purchase this at the Clock Town Bomb Shop for 50 Rupees so you can hold 20 Bombs at one time.
Big Bomb Bag - Save the Old Woman from the burglar in North Clock Town on the first night, this will be on sale at the Bomb Shop on the second day. With it you can hold a capacity of 30 bombs.
Biggest Bomb Bag - Turn into a Goron and talk to the Akindo Nut in Mountain Village, trade in your Big Bomb Bag and 200 Rupees for the largest and best Bomb Bag that can hold 40 Bombs.