Regardless of whether the bullet left the gun because of the force of a spring, the expansion of compressed gas, the expansion of gases caused by the burning or explosion of a chemical propellant, the primary energy component is kinetic. It may also have been heated, and of course there is a potential energy component, but those are minor considerations.
Jim's points on units of energy and power are on target. When I was in school, we spoke in terms of kilogram meters per second squared; that is the same as joules. Note that both meters and seconds are squared.