Go to sub urban bus stand. Take a bus for Ooty. Ask the station master or bus driver. Thats it. I would suggest you to go early in the morning cause they have safari till 9 am, I am not quite sure about it. Other time is from 3 pm to 5 pm. You can try that but if you are a trainee, then you have to hurry, you know what I mean.
Yes you can find direct bus. Govt buses run from Mysore to Ooty which go through Bandipur. You can get down at Bandipur. But at evenings there will be very less road services available. Happy travelling :)