The first decision you would need to make is if to travel from Goa to Mysore by bus or train. It's tricky! This is a 600km plus journey.
The good thing about bus is , you can get many direct overnight buses to Mysore from Goa (Panjim & Other places in Goa). AC (Volvo) ticket prices hovers around Rs1200. If you are not booking in one of those luxury buses, the journey is a bit tedious, in the regular bus. Ticket in the regular buses are relatively cheaper, around Rs600
The train option, though a bit longish and a bit circuitous in some cases, has the advantage of comfort once you boarded the train. Check out the Goa to Mysore Train options. Many alternate routes and options to get connections to Mysore are detailed with train route maps.
In addition to the regular bus options, this summer you can opt for the special summer trains between Goa and Mysore.
The route and stops of the summer special train is : Mysore City ---> Krishnarajanagar----> Holenarasipura ----> Hassan ----> Arsikere ----> Birur -----> Davangere ----> Ranebennur -----> Haveri -----> Hubli -----> Dharwad ----> Alnavar ----> Londa ----> Castle Rock ----> Kulem ----> Sanverdem ----> Madgaon ----> Vasco da Gama (Goa)
Altogether the railways will operate 4 trips in each direction. The first service from Mysore is on May 16, 2011 and the last service is on June 6, 2011. The train (Train No: ) leaves Mysore every Mondays ( on May 16,May 23,May 30 and Jun 6 ) at 3:15 pm and arrive at Vasco-da-Gama at 6 am, the next day.
Similarly towards Mysore the train (Train No. 06202 ) leaves Vasco-da-Gama on Tuesdays ( on May 17, May 24,May 31 and Jun 7 ) at 8.45pm and reaches Mysore at 11:35 am, the next day.
The distance between Goa (Vasco-da-Gama) and Mysore is about 700km. Second class sleeper ticket costs Rs275, 2nd AC and 3rd AC are Rs1018 and Rs742 respectively. This compares very well with the bus options you have between Goa and Mysore. The AC Volvo type bus ticket in KSRTC cost about 700 rupee one way and the regular express bus (Karnataka Sarige) about 200 rupees. Bus takes about 15 to 16 hours. KSRTC buses operate between the Mysore KSRTC bus stand and Panaji(Goa).
For train you can reserve seats online at the www.irctc.co.in portal by the Indian railways; for KSRTC seat online reservation (KSRTC Booking) log on to the www.ksrtc.in
And of course please check with official portals for the accurate fares,schedules and other details.