I did Bangalore - Belgaum on my Bullet in October. There were approx 50km of bad roads in total of the entire distance. I managed to do it in 9 hours including stops for Breakfast & Lunch. You should be able to do the distance to Mumbai in well under 15hours in a car.
I started at 6am from BG road and reached Blgm at 1515. There was a nice traffic jam near Peenya so early in the morning an i didn't expect it.
I suggest you start at around 4am rather than 2 or 3.
I couldn't spot any Shell bunks en-route till Belgaum. But there ought to be on the highway. You could rely on Reliance though.
Shell in India - Shell Station Locator