There are no direct trains from Bangalore to Indore.
The only way you can reach Indore is by traveling to a nearby station and getting a bus from there. You can either opt for Bhopal Junction (171.51 km by Road from Indore) or for Ujjain Junction (56km by Road from Indore) by train. Then you can choose to travel by bus, as there is good connection to Indore from these junctions by bus. From Banglore there are many direst Trains to Bhopal. There are many private travel agencies that provide buses (Volvo Rs 600 and above) to Indore. From Ujjain there are also buses provided by the public transport companies. Many buses of GSRTC travel via Ujjain and Indore. The bus route from Ujjain to Indore is shorter as well as cheaper (Rs 158 to Rs 256)
For trains from Bangalore to Bhopal go to Trains Bangalore Bhopal.