Below is the list of bombs in The Witcher 3. You are able to carry 2 bombs of each type at the start. When you upgrade them to Enhanced, you are able to carry 3 of each, and 4 when you upgrad them to Superior. In the alchemy tree, there is a category called “Bomb Creation” allowing you to upgrade your bomb arsenal like carry more bombs and deal additional damage.
To use a bomb, you need to slot it first in your inventory. Then use the Quick Access menu and select the bomb to throw it.
You can get bomb recipes either from chests or buy them from merchants. Below I list some possible locations of where you can get the bomb recipe. Unfortunately, there is a chance chest contents will be random or the merchant has a different items for sale.