The Jetfoil is Y6090 one way and Y10,990 round trip. It takes about an hour each way. The last return Jetfoil ferry to Niigata is around 5:00 PM although if you miss that, the last regular ferry returns around 7:30 PM getting into Niigata at around 10 PM.
http://www.mijintl.com/pdf/Sk2009all.pdfYou have to consider the time getting from Niigata station to and from the ferry port also. A taxi would be the fastest, otherwise, you would wait for a city bus in both directions.
You then have to find the bus in Ryotsu that goes to Aikawa (the bus station is under the ferry terminal), and once you're get to Aikawa, you have to get up to the gold mine, not a short walk. During most of the year, buses to the mines are only scheduled on weekends and holidays, I don't know about November. Regular buses on Sado are infrequent anyway and make a lot of stops. I would recommend renting a car on the island. You can check out Tocoo.com to see if they have any good deals for a day or two. For two people, the cost would be worth it.
If you made all connections perfectly, you 'might' be able to handle it in one day, starting with the 6 AM Shinkansen, arriving in Niigata at 8:16, using 30 minutes to get to the ferry and getting reserved tickets on the Jetfoil for the 9AM ferry, arriving in Ryotsu at 10AM, finding the bus to Aikawa and getting back for the 5PM return ferry, but more than likely, it won't work. You might have to take the 10AM ferry and it might take 3-4 hours getting to the mines and back waiting for and riding buses. You would have to stay at least one night on the island to see anything.
Your JR Pass would only get you to Niigata Station; everything beyond that is non-JR.
