Stone-ground stopper are custom made to fit securely into their own bottle (and only their bottle). Set the stopper snug into the bottle, than with firm but cautious pressure twist the stopper a quarter down into its seat. This will usually seal the bottle from all leaking.
You can buy a roll of shrink wrap from Home Depot or Lowes or any hardware stores (or shipping stores) for $7-8 -- it's 5 inches wide 1000-1500' long. Just wrap the bottle all around paying extra attention to the area over top of the stopper to maintain a constant pressure preventing it from working loose or falling out.