Score increasing

Are you trying to increase the value of the score (and display the new value) or to move the position of the score on the screen?

If the former, do this:

     public Transform player;
     public Text scoreText;
     public int score;
          
     void Update () 
     {
          if (Input.GetKey("b"))
          {
              score += 1000;
              scoreText.text = score.ToString();
          }
      }

Be aware that this code is extremely poorly optimized and will result in considerable garbage generation as it will generate a new string every frame, 60 times a second. However, it should get you started. A more elegant solution would be to only update the UI when the score has changed (which, I suspect, need not happen 60 times per second) or to start a coroutine in response to the OnPointerDown event.

Also, you mentioned that you're looking for this to happen when the screen is tapped, but your code refers to GetKeyDown, which is looking for keyboard key events. You may want to look into Unity's Input.GetTouch or, as I mentioned, do a coroutine like this:

 public class InputDetector()
 {
     
     public Text scoreLabel;
     bool isTapped = false;
     int score;
     
     public void OnTap()
     {
         isTapped = true;
         StartCoroutine(UpdateScore());
     }
     
     public void OnUnTap()
     {
         isTapped = false;
     }
     
     IEnumerator UpdateScore()
     {
         while (isTapped)
         {
             score += 1000;
             scoreLabel.text = score.ToString();
             yield return new WaitForEndOfFrame();
         }
     }
 }

Drag the OnTap() and OnUnTap() methods into the inspector's corresponding events (OnPointerDown and OnPointerUp respectively) and you're all set.