How can I remove the store from public without disabling plugin

You cannot disable the store plugin without losing all of your information. As you disable the store it removes the database tables that it installed. You can always remove the page with the shortcode on (or just delete the shortcode). Once you put the shortcode back the store will appear.

Do you know where the SQL hits are coming from? I would have thought that the hits to the store tables only happen when the store is in use.