There are no dungeons that require going through a spot that needs bombs. There are some cracked walls that can be blown up to get to extra areas. No doors need to be blown up. Doors may require a basic key, a gold key, or defeating certain enemies in the room before they will open. There are also one-way doors, such as when you enter a dungeon you cannot go back to the starting room.
If you post a screenshot we can let you know what is needed for the specific room you are in.