Mysore has three main bus stands (for state run buses) and a municipal bus stand for the private bus operations. The Mysore KSRTC Bus Stand ( Mofussil) and the Mysore City Bus Stand (city services) are the major bus stations in Mysore.
First let us get some idea about the KSRTC bus stand. All the interstate, intercity and other long distance buses operate from here. Only the state run ( Karnataka and also the neighboring states) buses operate from the KSRTC Bus stand. The most frequent service is the Mysore-Bangalore bus service. In every 5 minutes or so a bus leaves for Bangalore. There are different types of services to Bangalore. One of the most sought after (and expensive too) is the Airavata Service ( "Volvo Bus"). That is mainly, this type of service to Bangalore is fast,frequent and also comfortable.
The next popular bus service to Bangalore from Mysore is probably the Rajahamsa service. These buses are not AC like the Airavata buses. But Rajahamsa buses are more economical and fairly comfortable. These too operate at good frequency. But it takes longer time to reach Bangalore comparable to Airavat buses.
And then there a host of less luxurious (cheaper and slower) bus services too to Bangalore.
There are a good number of buses to Mangalore from Mysore. They are not as frequent as the Mysore to Bangalore bus services. But you should be able to catch a bus in 30 to 60 minutes interval that is heading towards Mangalore side.
Apart from the above you can get buses to Madikeri,Hassan, Dharmastala, Belgaum, Hubli, Shimoga and so on from Mysore.
For details on the schedules, services etc you can check the KSRTC official website (www.ksrtc.in) .
The city bus stand is located at a corner of the Mysore Palace compound near the KR Circle. The local services (city services) are operated from this bus stand. Apart from the regular buses, Mysore City has a good number of AC buses ("volvo buses"). Generally all the bus routes radiates out of the city bus stand, though there are some circular routes, eventfully end in the city bus stand. Buses are with route numbers ( displayed in the front and back top boards of the bus).
Most of the newer buses have scrolling electronic display outside, showing the routes also. Display is both in Kannada and in English. The city services in Mysore is one of the most efficient bus services you would find in any comparable cities in India.