If you are planning to do the Badami-Aihole-Pattadakal circuit, plan it well in advance so that you are comfortably placed with hotel bookings and transport tie-ups. You need to decide on which temples to look at too!
In case you are travelling by bus or in your private vehicle from Bijapur in the north by road, you could choose either the Bagalkot route or the Kerur route. From there onwards Aihole and Pattadakal will be only another 50 Km away. You could easily seek local bus service from Badami or take a hired auto rickshaw or taxi to move ahead. Costs are reasonable and availability is great!
Please keep in mind that you might find getting a night lodge quite hard in both the small villages of Aihole and Pattadakal, so you should catch up on your sleep overnight at Badami. In fact even in the morning when you wake up at Badami, you could consider keeping this your base station to finish the rest of your tour! In case you wish to move onto Pattadakal from Badami, you will find it is only half an hour away. A little ahead from there and you will reach Aihole in another 20 minutes. Alternatively, you could also gain entry into Badami from Hubli, Gadag or Hospet in the south.
You third option of getting into Badami is if you come via a small detour of Hampi. From there you could hitch a bus ride to Ilkal from Hospet and proceed to Badami. Ilkal is on the Bijapur highway. After this, change over to Badami. Else, you can consider going to Gadag and boarding a bus to Badami. Whichever option you try, you should reserve a good 4 to 6 hours. Keep some buffers for delays in the bus commencing its journey for logistic issues. You will spend close to 4 hours travelling between Hospet and Badami. Safest option is to board KSRTC buses. There are in plenty that ply between Badami with Bangalore. You can rely on the railway station at Badami since Pattadakal does not have one of its own.
Golgumbaz Express (Train Number 6535 / 6536) is a tri-weekly express train between Solapur and Bangalore( Yesvantpur Junction). In the Yesvantpur to Solapur route it is called Solapur Express and in the return route it is called Golgumbaz Express.