Start early from Mumbai by overnight train or flight (flight recommended for speed), reaching Baidyanath Jyotirling by noon. The cost for flights from Mumbai to Deoghar (nearest airport) is approx INR 4,000 per person one way.
Take a morning flight from Deoghar to Bhubaneswar via connecting flight at Kolkata (approx total travel 6-7h including layover). Flights approx INR 5,000 per person one way.