Top Down Bullets will not move

Question

I have a top down shooter. The player can move in the primary 4 directions, and follows the mouse for rotation.

When I shoot, the bullets never leave the player, they just spawn on top of the player sprite.

I have tried a combination of velocity and AddForce methods, but I don't understand why the bullets never move. I have tried moving them in the Bullet's script or in the calling WeaponAttack script that Instantiates the Bullet.

Side note for educational purposes: Which method is better? Should the bullet govern its direction and velocity or should the Instantiating class govern it?

PLAYER ROTATION SCRIPT

public class RotateToDirection : MonoBehaviour {

    Vector3 mousePos;
    Camera cam;
    Rigidbody2D rid;

    void Awake () {
        rid = this.GetComponent <Rigidbody2D> ();
        cam = Camera.main;
    }

    void FixedUpdate () {
        rotateToDirection ();
    }

    private void rotateToDirection() {
        mousePos = cam.ScreenToWorldPoint (new Vector3 (Input.mousePosition.x, Input.mousePosition.y, Input.mousePosition.z - cam.transform.position.z));
        rid.transform.eulerAngles = new Vector3 (0, 0, Mathf.Atan2 ((mousePos.y - transform.position.y), (mousePos.x - transform.position.x)) * Mathf.Rad2Deg);
    }
}

WEAPONATTACK (SHOOTS THE BULLET)

public class WeaponAttack : MonoBehaviour {
    public GameObject bullet;
    public GameObject player;

    public float bulletSpeed;

    void FixedUpdate () {
        if(Input.GetMouseButton (0)){
            attack ();
        }

    }

    public void attack(){
        Instantiate (bullet, player.transform.position, player.transform.rotation );
        //Rigidbody2D bulletInstance = Instantiate(bullet, transform.position, Quaternion.Euler(new Vector3(0, 0, 1))) as Rigidbody2D;
        //bulletInstance.velocity = transform.forward * bulletSpeed;

        Physics2D.IgnoreCollision(bullet.GetComponent<Collider2D>(),  player.GetComponent<Collider2D>());

    }

}

BULLET

public class Bullet : MonoBehaviour {

    public float moveSpeed = 500.0f; 
    private float killTime = 1.0f;
    private Rigidbody2D body;

    void Awake() {
        body = GetComponent<Rigidbody2D> ();
    }

    void FixedUpdate(){
        killTime -= Time.deltaTime;
        if (killTime <= 0) {
            Destroy (this.gameObject);
        } else {
            body.position = body.position * moveSpeed * Time.deltaTime;
        }
    }

}

Answer 1

    GameObject bulletInstance = Instantiate(bullet, transform.position, player.transform.rotation) as GameObject;
    bulletInstance.GetComponent<Rigidbody2D> ().velocity = transform.right * bulletSpeed;