Since nobody else has answered yet, I hope this helps. I don't use a controller.
You need to load the bombs into your quickslots (the ones on the top right of your inventory screen) before fighting. There are five slots.
In the main screen, the currently selected bomb shows next to the currently selected sign, in the bottom left of the screen. To change to a different bomb before or during battle, bring up the quick menu (LT?) and select it from there.
To throw the currently selected bomb, use RB