The journey from Gangtok to Mysuru covers roughly 2500 km. You must first reach NJP or Bagdogra. From NJP, you can take a long-distance train to Mysuru Junction. Flights from Bagdogra to Mysuru usually connect through Bangalore.
Total Distance: 2500 km by road, 2000 km air distance.
This is a very long journey; ensure you have a confirmed berth.
Bangalore is the most convenient hub for this connection.
October to March for pleasant weather.