Cook potatoes until a knife can penetrate to center of potato (potatoes will cook further on the grill). Cool. Cut potatoes into ½-inch thick slices. Toss gently with ¼ cup chunky blue cheese dressing. Grill potato slices. Cool thoroughly; cut into chunks.
Combine remaining 1 cup chunky blue cheese dressing, mustard, celery, green onion, bacon and black pepper in a bowl. Pour over potatoes and toss gently to combine. Sprinkle with parsley and chill.