The bullet train, or Shinkansen, is a great choice.
There is a direct service between Niigata and Tokyo on the Joetsu Line. The fare, one way, is 10270 Japanese Yen. At the moment, that's about GBP�52 or US$90.
Japanese trains are a marvel - they run on time, to the second and they are spotlessly clean. You'll have much more room on a Shinkansen than you would if you flew or took the bus.