Mysore palace is located right in the heart of the city. The city bus stand is located at a corner of the palace. In fact the Myosre city bus stand and the palace share a common wall.
The mufesal bus stand - the KSRTC Bus Stand - from where long distance buses are operated is located at couple of kilometers away from the palace.
In fact it is possible to walk from the bus stand to the north gate and the east gate of the palace. Its about 1 kilometer(½ mile ). The south gate is another 1 kilometer (½ mile ).
Note that the ticket counter is located at the south gate. A road and a footpath goes around the outer wall of the palace compound.
From the bus stand area to the palace ticket counter it is about 15 minutes ( Rs 15 to 25) ride by an auto rickshaw.
The Mysore railway station is relatively far from the palace, with respect to the bus stand ( 2½ km /1½ mile ). Hire an auto rickshaw to the palace. Or you can even catch a city bus to the palace locality.
Mysore city is well connected by other major towns and cities of Karnataka by train and bus. Also there are frequent interstate bus services from Mysore to many cities of Tamilnadu and Kerala.
Bangalore to Mysore is a well connected and busy route. Mysore airport is relatively new and less busy, only chartered flights operate.
If you are heading towards KRS Dam (Brindavan Gardens) , Ranganthittu bird sanctuary, GRS Fantasy Park, Hunsur , Coorg etc take the right at the Outer Ring Road junction (this is a large junction at the Colombia Asia Hospital with traffic signals, giant sign boards with route directions etc).