It would probably be similar in role to the hot air balloons used by the OTL Union Army in the American Civil War. In fact, said balloons were the inspiration for the Zeppelin!
As for how the union used said balloons, they were mostly used for reconnaissance, as they could see far away from their high vantage point. However, they had trouble communicating with the army on the ground below.
As for using them how one would use a bomber aircraft, they would likely be a very big target for artillery and even long range guns, forcing them to fly at high altitudes as any hit to the hydrogen cells would make the airship explode. I don't think an early Zeppelin's density would be low enough to fly high enough to avoid enemy fire, making them pretty useless for anything other than recon.