Ooty is just around 125 KM away from Mysore, so it's a good choice for a short trip from Mysore.
Ooty does not have main-line railways. So train is not an option. Road transport is the only way to reach Ooty from Mysore. There are frequent buses plying between Mysore and Ooty. Roads are in good shape, so the bus journey is quite comfortable.
There are quite a few bus operators for Mysore-Ooty journey, but the state-run KSRTC is the best in terms of service and punctuality. You can get KSRTC Volvo buses from the Sub-urban Bus Stand in Mysore. KSRTC operates 10-12 Mysore-Ooty trips daily on Volvo buses. Volvo buses take around 4 hours to reach Ooty from Mysore. The fare is around INR 450 in KSRTC Volvo Club Class. There is no need to book tickets in advance. You can simply go to the bus stand and board an Ooty bound bus. Online booking facility is also available on ksrtc(.)in.
A cheaper option is KSRTC Rajahamsa. These are non-AC semi-sleeper buses with push-back seats. The fare is around INR 300 and the journey takes around 5 hours. KSRTC also operates ordinary buses (Karnataka Saarige) between Mysore and Ooty. I am not sure about the exact fare, but it should not be more than 200 bucks.
Another option is the SETC Ultra Deluxe bus service. SETC buses depart from the other side of the same bus stand. The price is around INR 300 per ticket. Journey duration is around 5 hours.
TNSTC too operates buses between Mysore and Ooty from the same bus stand, but that should be your last option. These are old model ordinary buses with uncomfortable seating. On top of that, these buses stop at all possible towns en-route, extending the journey time to 6-7 hours. Fare should be below INR 200.
For a more comfortable ride, you can book a taxi. In terms of cost, it would be quite expensive though - no less than INR 3000 for one-way trip. If you are comfortable driving in the hill sections, then I would suggest you to rent a self drive vehicle either from Avis or Myles. It would be much more convenient than hiring a taxi and would come at a cheaper cost. You won't even need to hire a taxi for the local sightseeing in Ooty. As already mentioned, the roads are in great condition and driving is a real pleasure.
Regards,
Deb