Mysore and Ooty (Nilgiris in Tamilnadu) makes two ideal pair of destinations. Ooty is south of Mysore. These are well connected adjacent districts. You can also add a couple of other attractions en route. The highlight of the travel is crossing the wildlife sanctuaries (Bandipur National Park & Mudumalai Tigre Reserve ) part of the Western Ghats .
The most popular means to travel from Mysore to Ooty are by bus and car.
There are many private tour operators and the the state run KRSTC that operate regular bus services to Ooty.
Check out the routes options to travel from Mysore to Ooty.