Buses to Mysore are operated from the KSRTC Satellite Bus Station on the Mysore Road. If you are flying into Bangalore there is a direct Bangalore airport to Mysore bus service called Flybus, operated by KSRTC.

The Satellite Bus Station is about 5 km from Bangalore City railway and the Kempegowda Bus Station. From the bangalore airport (), the Satellite Bus Stand is about 40 km, towards south west (towards the direction of Mysore)

You need to travel by the local city bus or private taxi/auto-rickshaw to travel from the city Kempegowda Bus Station/railway station, it can take around 1 hour thanks to the slow-moving city traffic.

Inside the KSRTC bus stand there is a separate platform for the Bangalore-Mysore bus services. The ticket counter is next to the platform. Book online in advance (www.ksrtc.in) to ensure you get a seat , especially during the weekend and other peak seasons.

There are less number of buses now operate from the Kempegowda Bus Station (Majestic), located opposite to the Bangalore City railway station.

Also there are many long distance (Airavat, Airavat Club Class and Rajahamsa) buses via Mysore start from the Shanthi Nagar Bus Stand in Bangalore city.

Bangalore Mysore Bus fare:
There are different types of services to Mysore. The highest class is the AC buses called "Airavat" services or popularly the "Volvo Buses". There are also a few Mercedes- Benz services by KSRTC from the same platform.

Airavat fare is Rs270 and Airavat Club Class fare is Rs300 one way.
The Rajahamsa class services are non AC, but with pushback seats. Ticket costs about Rs210.

Ticket for the regular express service ( called Karnataka Sarige) cost about Rs132.

If you are keen, see the train fare also from Bangalore to Mysore.

They play those old bollywood blockbusters, or its local genres, in the Airavat and Rajahamsa services. If this is not your idea of on board entertainment , get to the back rows. In the Volvo and Mercedes- Benz buses traveling in the last rows is not a problem as the suspension is pretty good. However in Rajahamsa and other lower services avoid the last few rows ( beyond the rear axle), as the ride could be a lot bumpy.

On the other hand the front row in the Airavat bus is a superb location to enjoy the sights while traveling.

There is a ticket counter at the platform. Many times they issue tickets at the counter. Otherwise the conductor directs to get inside the bus and issue tickets inside the bus. Seats are occupied on a first come first served basis. A bus leaves when it is fully occupied. During the weekends and other holidays you'll find long queues at the ticket counter.

The frequency/timings  of service is fairly good between 6am and 8pm. After that you can still get in a long distance bus that passes via Mysore (to Coorg, Mangalore, Kerala etc ). Those buses leave from a different platform located in the main building. Check at that inquiry counter in the main building about the availability of service, platform location etc.
Inside Mysore city, the bus drops you at the Mysore KSRTC bus stand (Central bus stand). You can catch a return bus to Bangalore (or for other cities) from the same bus stand.

City buses stop at  the corner around the bus stand. Walk out of the bus stand to catch the local bus. The city bus stand is a couple of km away around the corner of the palace.

As you come out of the bus agents/touts would pester you  (if you look like a tourist!) with various services (hotel,taxi,sightseeing etc). Neglect.

If you are not very familiar with the city/language etc go for the prepaid auto rickshaw for local travel. There is a prepaid auto rickshaw stand next to the gate through which your bus entered the bus stand.  Tell your local destination (they have a standard list ) at the counter and get the print out. This mentions your destination, the fare to be paid to the driver and also the registration number of the rickshaw. Keep a one rupee coin handy as this is the service fee to be paid at the counter. Retain the printout with you. This is your copy, do not hand it over to the driver. All you need to do is pay the driver - at the end of the journey - the amount mentioned in the printout.

By the way there is a similar prepaid counter inside the Mysore Railway station too.

You may also wants to check the train options to travel from Bangalore to Mysore.