Bangalore to Mysore: It’s about 150 km drive on the state highway (SH17).
The highway is in good condition, with 4 lane most of the way. You’ll take anything between 3 to 4 hours, depending on many traffic conditions. What probably slows down would be the slow moving traffic in the Bangalore city to Bidadi stretch (about 30km). Beyond this traffic moves pretty smooth.
You'll pass Ramanagara,Maddur, Mandya and Srirangapatna before reaching Mysore.
There are also plenty of bus services (KSRTC) and train connections for Mysore from Bangalore.
See also : Places Near Bangalore : Towards Mysore