NullReferenceException after adding a script at runtime

Hi there! I'm working on a unity project for university with other students together. Each of us has to build a spaceship and a level with the intention that all spaceships are able to race in all levels. In my level I want the ships to be able to shoot stuff and I wrote a very simple script to allow this. As I can't add anything to the ships of my teammates manualy, I want to add the script to the ships at runtime if my level is selected. I have a bullet prefab that I use to clone the bullets and if I add my script manually to a ship it works, I can shoot. But if I add it at runtime, I get the following error each time I try to shoot:

NullReferenceException: Object reference not set to an instance of an object T4PlayerShoot.Update () (at Assets/T4/T4PlayerShoot.cs:35)

I guess after adding the script at runtime it loses the reference to the bullet.prefab. How can I fix this? Here is my relevant code: in my levellogic:

     void OnGUI() {
     //...
         var ship_objects = GameObject.FindGameObjectsWithTag("Ship");
         foreach(var ship_object in ship_objects){
             ship_object.AddComponent<T4PlayerShoot>();
             }
     //...
     }

the shooting script:

 public class T4PlayerShoot : MonoBehaviour {
 
     public Rigidbody bullet;
     public float velocity = 10.0f;
     protected string fire;
     private bool firePressed = false;
 
     //Get the Firekey of the Controller
     protected virtual string FetchFire(Controller controller)
     {
         return controller.ctrlAxisFire;
     }
 
     private string FetchFire0()
     {
         Controller ctrl = GetComponentInParent<Controller>();
         if (ctrl != null)
             return FetchFire(ctrl);
         return null;
     }
     
     void Update () {
 
         if (fire == null) {
             fire = FetchFire0 ();
         }
 
         if (fire != null) {
             firePressed=0!=Input.GetAxis(fire);
         }
         if (firePressed) {
             Rigidbody newBullet=Instantiate(bullet,transform.position,bullet.rotation)as Rigidbody;//ERROR
             newBullet.AddForce (transform.forward*velocity,ForceMode.VelocityChange);
         }
     }
 }

Thanks for your help!