Badami via the shortest route is about 450 kms however if you are driving down it is better to take the Hubli route. Although the route is longer by about 70 kms you will be able to avoid the long lines of trucks and traffic jams in Hospet and surrounding areas..
Bagalkot is the nearest railway station from Badami. Badami is about 35 kms from Bagalkot. There are numerous buses plying between Bagalkot and Badami
Badami is about 520 kms from Bangalore via the Hubli route which is advisable due to the long lines of trucks and traffic jams you might encouter in the Hospet route.