Hello,
There is no direct transport mode connectivity between Mumbai and Hampi. The cheapest way to reach from Mumbai to Hampi is bus to Bangalore, then bus to Hampi and takes 24h 45m. The fastest amd recommended way to reach from Mumbai to Hampi is flight to Hubballi Airport, then cab to Hampi and takes 6h 13m. Cheers ✌️
Best is to fly to Bangalore and take a bus / cab from there (350 km, 6 hours), ideally plan for 3 days including half day visit to Hire Benkal (50 km).
Hampi located on the banks of Tungabhadra river was known as Pampa kshetra. Hampi was the capital of Vijayanagar dynasty which is a UNESCO World Heritage site. Flying to Bangalore from mumbai taking a bus to Hampi takes a day to reach. While flying to Hubballi airport from mumbai and taking a cab or bus makes reaching easy for 6 hours away is Hampi.