"Bulge" is typically used to refer to a convex/raised deformation of a material relative to the viewing/reference surface. "Dent" is used to refer to a concave/lowered deformation. An outside bulge viewed from the inside of the barrel is a dent and an outside dent viewed from the inside is a bulge.
The outside bulge usually gets there when a bore obstruction causes a gas hammer that raises local pressure high enough to create a local force above the elastic limits of the steel. The bulging of the steel raises the elastic limit of the steel (cold working) and drops the local pressure (increasing volume for the gas to expand into) which drops the local force. When the gas pressure drops back to atmospheric upon exit of the ejecta, the local area of the bulge is not able to return to original dimensions due to being plastically deformed.
An outside dent usually gets there by the barrel being struck against a hard object with sufficient force to exceed the elastic limit of the steel in the area of the strike. Metalurgically speaking, the steel doesn't care if you think it is a bulge or a dent. The steel only knows that it got stretched more than it can stand and it is not going to "snap back" to original dimensions. To get it back, you will have to apply sufficient force in the opposite direction to overcome the new strength just enough to return it to original size and shape. Thus, the return force is usually a series of smaller, carefully controlled and more localized forces rather than one force as was the first deforming force; tap it back in place.
The hazard here is that very sharply deformed metal may not go back in place exactly. Examples would be a dent formed by a sharp edge that "creases" the metal or a bulge that has a sharply defined perimeter. In these cases, the metal may have used up much of its fatigue strength and later fail under uormal flexing (a shotgun barrel expands in diameter each time it is fired). A skilled repairman will have a good feel for how the metal is reacting and if it will behave itself in the future.
