This sounds like an exciting road trip!
For the best route, take NH4 till Tumkur, folllowing which take the state highway till you hit the Bangalore-Mysore Road. Go till Mysore, then head to Ooty. Drop in at the Bandipur National Park on the way maybe?
Do have a meal at Kamat Madhuvan on NH212 in Mysore (Masala Dosa, and a cup of tea for me!).
Have a good one!