Getting bombs in Ocarina of Time was always a great moment, and Nintendo have utilised it even more in the new remake by creating even more places for you to blow up using them. I really like how the rocks have little cracks that the bombs sit in now if you throw them right; it's just little touches like this that make the game even more pleasurable to play.
But I'm getting ahead of myself - you came here to find out how to get a bigger bomb bag so that you can hold more explosive power!

The bomb bag that you get in Dodongo's Cavern looks so much cooler than the previous one, but I can and have said that about everything so far. It's made from the stomach of a Dodongo, and it holds 20 bombs.
But 20 isn't that many when you're out in the field causing destructive mayhem. If you want to get a bigger bomb bag, then you can get it straight away by heading into Goron City.

There's a sign that tells you that if you can stop a rolling Goron at the perfect place, you'll get something special. Wait for the rolling Goron to get near the sign, and put down a bomb right in its path. The bomb will explode, stunning the Goron for a few seconds. When he comes to, he tells you that he's impressed you stopped him in the right place, and he gives you a bomb bag upgrade.

This bigger bomb bag holds 30 bombs in it, which is a nice little upgrade to have, but you can still go one better.

Head to the Bomchu Bowling Alley in Hyrule Castle Town. It opens up once you complete Dodongo's Cavern and the Gorons start to bring bombs back to Castle Town. It's a game where you fire Bombchus towards targets, with obstacles in the way.
I completed this once and got a heart piece, but on the second try, I got the biggest Bomb Bag, holding 40 bombs inside it. That should give you a lot more firepower when you're heading into dungeons, meaning you don't have to call on Business Scrubs as much!