You should probably use a combination of dead reckoning and timestamped messages for that kind of game.

Let me see if I got it right:

When connecting to the server your local time will get sync'ed to the server's.
Your client's time will be about PING milliseconds behind the server's. When you send a "shoot bullet" message to the server, add your local timestamp, position and direction. When the message arrives at the server it can look up how the gamestate was at that time (the server's time will be about 2*PING in the future at that point) and see if the shot hit something.

Feel free to correct me. Haven't done this for some time.