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Mumbai to Goa is about 600 kms. So, you'll leave in the morning and expect to reach by late afternoon. It should take you about 10 hours if you're really fast enough, counting the breaks in between too.
Goa to Bengaluru is approximately same too.
A 4 AM to 4 PM plan should be it, I guess, excluding the route choice difference.

Members, kindly help Gahlaut with the route choice and other matters.

thanks, I ended up taking NH4 for the journey. Its fairly scenic as well, though gets boring after some time. After a place called Nipani, I decided to ditch the NH4 and turned right on to SH135 hoping for some more scenery given i had the luxury of time. The roads are bad, and it winds in and out of villages, however it is really picturesque. Would recommend the SH to anyone who is not constrained by time and doesn't mind bumpy roads.

Took about 6 hours to reach Nipani, and after that took another 7 hours on the SH.

Left Goa next morning at 6am and again took the state highways, this time a slightly different route, which had ever worse roads and was even more scenic. There was no one on the roads but me for fairly long stretches (10kms or so at a time). Got stopped by a cop along the way who thought I was smuggling stuff out of goa through the backroads and had to open out all my luggage on the road to convince him otherwise.

All in all, would recommend state highways in and out of goa if you have time on your hands and don't mind rough roads...one of the more scenic routes i've seen.

Hey, nice ride. Im doing Mumbai to Goa in December. I will be taking the NH 17 though. Roughly how much time did it take you?

Advise you take the NH4 route, whilst scenic the NH17 is a death trap, I have done the NH4 route around 12 times now in the past 4 years, though only by car, from Bombay to Goa the best I have managed is 8hrs with less than 25 mins breaks, the worst has been 10.5 hrs with many breaks, best is to leave around 7-7.30 am and reach before sunset, allowing enough time for breaks.