KSRTC (karnataka state road transport corp, the state bus service) runs about two dozen buses daily between Madras and Bangalore. They get you from city center to center. Consider the Airavata or Mercedes Benz Buses. Here's the daily schedule. Take your pick. Cheap in comparison to the train or air. Here's the KSRTC fleet detail. There even seems to be a bus with "sleeper" berths (Corona AC sleeper)!

There are also private bus operators between the two cities. I have never taken them.

Of course, the Bangalore Airport is way out and the drive into the city can take between 90 and 120 minutes (similar time heading back to the airport). THat's caused a surge in people taking the train or buses or simply driving down to Madras.

If you want to get to Bangalore by lunch time, you will have to leave Madras by 0600 (Shatabdi) or 0630 (KSRTC Airavat). The flight options are really unviable imo given the Bangalore Airport's location.