There is a small station in Badami which is located 5 km from the center. Trains from Bangalore, Bijapur and other cities stop there regularly. From the station, there are many rickshaws to reach the center. You can also wait a bus which goes to the bus stand. It will cost you only Rs. 3.
From Mumbai, there are two options. Take the Hussainsagar Express to and change at Solapur Junction (Arrives at 5.25 AM) to the Solapur-Hubli (Departs Solapur at 6.25 AM) Express. Alternately, take the Chalukya Express (Mumbai to Puducherry) to Hubli Junction and change to a Solapur bound train from Hubli. One can also take the Mumbai Bijapur Fast Passenger, but that runs only 4 days a week.
The bus stand is located in the center of the town. There are buses for [wiki=71a50caf8a022a6220c6bd0912f47b4a]Gadag[/wiki], Bijapur, Bangalore and [wiki=b1468198e60cdba513617114bee9a40c]Hospet[/wiki].