Buses are reliable but with only 9 hours at your diposal that method would waste a lot of your precious time. It takes time to get up the cliff and back down again. (PLEASE DON'T RIDE THE POOR ABUSED DONKEYS!) An ATV is a good option as long as you're skilled and it has enough power to take you wherever you want to go. Some don't, so choose carefully. There are car and rental agencies close to the cable car building where you will be coming up the cliff from the tender dock. As you exit the building turn left and walk to the end of that short lane. Turn right and you'll see a short flight of steps ahead on the left. Walk down those steps and out to the main road, about 100 yards. You'll see rental companies right there. I can recommend Tony's. You have to turn left and walk uphill a short distance to find his office. Or you can contact him on the internet and ask for someone to meet you at the cable car building. Same goes for any other rental agency you might contact.
If you think you might rent a vehicle be sure to go to your local AAA office to pick up an International Driving Permit, no test or membership required. Bring 2 passport photos with you to save a few dollars. A rental agent may not ask for it but Greek law requires it, and if you get in an accident without having one you'll be liable for any and all damages and your insurance will be invalid because you will have been driving illegally.