The reply depends on the question. "Would you like sugar with that?" should be answered with "Nein, danke" or Ja, bitte". If the question implies and action "Would you like me to pour milk into your coffee?", "Bitte nicht." would also be a good option. The complete sentence would be "Bitte tue das nicht", or "pleas do not do that".
Is "Nicht, bitte" really incorrect here? I got the impression "bitte" was pretty much always last in the sentence...