Bomb Expert is a Survival Skill in The Last of Us, available as a part of the Professional Survival Skills Bundle. The description reads: "Your bombs will explode more quickly and you'll be immune to the stun of your own smoke bomb as you level up this skill."
Level 2 (3 loadout points) - Placed bombs, thrown smoke bombs and bombs have an even shorter fuse.
Level 3 (5 loadout points) - You are immune to the stun of your own smoke bombs. Placed bombs, thrown smoke bombs and bombs have a very short fuse.
Bomb Expert ensures that enemies are less likely to escape smoke bombs and nail bombs.
Bomb Expert works well with Explosion Expert; the combination of a larger blast radius and the shorter fuse makes escaping nail bombs much more difficult. Bomb Expert 3 also works well with Covert Training, as it allows users to stun enemies with smoke bombs and shiv them without worrying about stunning themselves in the process.
Bomb Expert 3 works well with the Flamethrower in close quarters, especially against multiple opponents. The flamethrower has a slight delay when starting up and downing enemies. The stun from a smoke bomb can give time to spray multiple enemies with flamethrower, as well as providing cover. This strategy can act as a pseudo-multi-shiv, because there is no chance of recovery (instant execution) and the user does not appear on the minimap.