Hi Manjunath,
By road: This route will take a little over 9 hours - Bangalore - Karmali - Dudhsagar (633km).
By air: Fly to Goa. From the Dabolim airport, its a 2hr drive to Dudhsagar. By rail: The Rani Chennamma Express (16589) from Bangalore to Londa Junction or a direct train to Castle Rock, the Mas Vasco Express (17311). Accommodation: 8km away from Dudhsagar, the Jungle Book Goa is a good option. (http://www.booking.com/hotel/in/jungle-book-goa.en-gb.html?aid=817014)