Coorg is called the Scotland of India, and you will understand why when you visit this place. It is a 120-km drive from Mysore.
My friends and I rented a couple of bikes from Mysore. For each of us the cost was only around 1k. We did not roam around much since we were tired. I would suggest you to take a local bus from Mysore to Coorg and rent a bike in Coorg. This way, you can go to a lot of places with the same budget of 1k per head, including petrol. You can drive around 350 km. We had put petrol for Rs. 700, which was more than enough for 350 km. Take geared bikes, since at some points, there will be steep uphill roads that the non-geared vehicles will find difficult to climb. There are many bends but the incline is negligible for the most part. You might find a few steep rises in the roads, and there are some turns where you should be careful.