Advice on learning to play a piece without the score?

If the music is your safety net, take a random score and put it in front of you when your playing, and be sure to show your teacher before hand that the random score isn't the real score, and is in no way severely related. That way, you have a fake safety net, but because you are focusing on the keys of the piano, not the music, your brain shouldn't be able to tell much of a difference.