Zeppelin? I think you mean the static observation balloon.
Zeppelins were made with a rigid metal structure. The observation balloons (used by both sides) were simply hydrogen-filled gasbags with the observer's basket underneath. They were always protected by anti-aircraft guns and since the gunners knew the altitude of the balloon they were protecting it was very dangerous for an attacking aircraft. In effect, it was like bait.
The balloons did valuable work photographing and reporting on enemy troop movements. It was important to knock out the enemy observation balloons as well as observation aircraft.
And yes, I always believed that actual bullets were used for that scene.

I can't confirm nor deny but the only place it might be practical is during the zeppelin shooting and since it was fixed by wires they could have easily run a wire to a charge attached to the zeppelin that they then detonated from the ground at the right time. That would be the normal and efficient way to do it.
So I would guess they didn't use live machine gun ammo.
Although during the German bomber scene where you see the bombs drop through the chute and hit the ground I could see where they might have used real bombs there.

No data to back it up, but I just watched that shot where he takes down the zeppelin sure looked like live ammo.