Bangalore to Mysore distance by road is about 140 kilometres.

The driving time and distance depend on where and when you are starting in Bangalore. It is typically a 3 hours drive, including a short break at one of those drive-in restaurants en route.

Let's split the route into 3 parts - Exit Bangalore City, drive on the expressway and enter Mysore city.

Exit Bangalore City:
This is the slowest part of the drive. There are two ways to exit Bangalore.

The first option is to take any of the radial roads that lead to the NH275 starting point in Bangalore city.
Or take the NICE road (NH48), which encircles Bangalore and intersects the Bangalore-Mysore expressway (NH275) in the southwest of Bangalore.

If you are driving from the northern, southern or northwestern areas of Bangalore, take one of the highways (NH44 / NH75) circling Bangalore & get to the NICE road (NH48, toll expressway). Take the Mysore exit on the NICE road, which is close to the entry of the Bangalore-Mysore Expressway.

In short, wherever you are in Bangalore, get to the NH275 junction that intersects NH48 where the Bangalore-Mysore Expressway entry is.

Typically this is a 1 hour to 1½ hours drive (30 to 45 km).

Drive towards  Mysore on the Expressway
This is an access-controlled highway to Mysore. From the expressway entry to exit at Mysore is about 117 km. You can cover this in about 1 hour 30 minutes. There are two toll plazas one near the Bangalore entry & other near the Mysore exit.

Keep everything in order before you get into the expressway, as there are only very few exits to reach fuel stations, restaurants and the like.
See the list of restaurants on this stretch & the exit points to reach them.

The expressway will end at the outskirts of Mysore city, where a ring road intersects the expressway. The NH275 further continues towards Mangalore via Coorg, but not as an expressway.

Enter Mysore City ( or Not!)
At the signal take right (NH275) for heading towards Coorg, Mangalore etc.

Take left for Ooty (Tamilnadu), Wayanad ( Kerala), Kollegal etc.

The straight road from the signal junction will reach the Mysuru city centre. From the signal to city center is 15 minutes drive ( 7 km).

Also, check out the train and bus options and the cab options to reach Mysore from Bangalore.