Hey the best route from Bangalore would be Bangalore-Mysore-Nanjangood-Bandipur-Madhumalai-ooty.
Since you will be changing states, you need to get a permit(you can get this at a RTO in ooty, if asked in madhumalai checkpost just say that you will be getting in OOTY), And the road passes through the jungle and the roads will be closed from 7 p.m to 6 a.m. so plan your trip accordingly
Good day, Cheers !!