Driving is the only way to do all twelve on your own timetable, and the only way to reach Bhimashankar and Srisailam without a bus. Shrine to shrine it is about 7,824 km; the calculator adds the drive out from your own town and the drive home, and stops short of the one shrine no car can reach.
Every leg with its real driving time, the ghat roads and forest roads that slow the circuit down, what fuel and tolls come to, and where a hired car beats your own.
The same circuit by rail: every train, the days it takes, and the fare per person by class.