even I go to goa couple of times in a year to visit our temple in Revana.
The route I usually take is through Hubli (My parents stay in this city).
Bangalore - Hubli (7hr drive) GQ
Dont enter hubli city, take the bypass road after the toll gate, [ask the person which left turn 1st or 2nd iam not sure] turn left towards Karwar. This will take you through
Kalgatagi - Yellapur - Karwar (172kms - 2.5 hrs) - Goa
Since the mines trucks are off road this will be the best route. instead of going through Haveri - Sirsi - Ankola route