Bomb Bag

The Bomb Bag is the case in which Link carries his supply of Bombs. In Ocarina of Time it is said that the Bomb Bag is made from the stomach lining of a Dodongo. It is often possible in Zelda games to acquire larger Bomb Bags as you progress.

Ocarina of Time
In Ocarina of Time you can get two upgrades: one as a prize in the Bombchu Bowling Game and one from stopping Hot Rodder Goron's wild rolling around Goron City's 3rd floor.

Majora's Mask
In Majora's Mask there is the regular Bomb Bag and the Bigger Bomb Bag. You can obtain the Bomb Bag by returning to normal, then going to the 3rd shop in West Clock Town. They will have the Bomb Bag in stock, and you can carry Bombchus and Bombs in it. The Bigger Bomb Bag is obtained by going to the Curiosity Shop on Night of the Final Day, around 10:00 p.m. . They will have the Bigger Bomb Bag there. OR you can save the old lady from Sakon the theif in North Clock Town at Night of the First Day, around 12:00 p.m. They will then put Bigger Bomb Bags in stock at the Bomb Shop by tommorow. This also allows you to get the All-Night Mask from the Curiosity Shop at 12:00 p.m. Night of the Final Day, for 500 Rupees.

The Wind Waker
In The Wind Waker, the bomb bag is not actually shown as a physical item, however it is still possible to upgrade the number of Bombs Link can carry by visiting the Great Fairies. Initially it can hold 30 bombs, with increases to 60, then 99.

Twilight Princess
In Twilight Princess however, this has been changed. In this game, you are able to receive an extra two bags, so that you have one for each type of bomb available, Bombs, Water Bombs, and Bomblings, of which you can first hold 30, 15, and 10 respectively, and which can be doubled to 60, 30, and 20 by scoring 25 or more points by playing Iza's River rapid Ride.

Image taken from Zelda Elements