AddComponent adds too many (C#)

My move script currently adds a bullet and adds the script BulletScript to the bullet when the user presses X.

The problem here is that it adds too many BulletScripts to my bullet game object. Like it's in an infinite loop or something.

Here's the shoot part of my move script

 void Update () {
     if(Input.GetKeyDown("x") &&  Time.time > NextFire) {
         NextFire = Time.time + FireRate;
         shoot.gameObject.AddComponent<BulletScript>();
         shoot = Instantiate(shoot) as GameObject;
     }
 }

And here's my bullet script

 private GameObject player;

 void Start () {
     player = GameObject.Find ("Player");
     gameObject.AddComponent<Rigidbody>();
     transform.position = new Vector3(player.transform.position.x,player.transform.position.y,player.transform.position.z);
     collider.isTrigger = true;
     rigidbody.isKinematic = true;
     rigidbody.freezeRotation = true;
 }