Public transportation on Corsica leaves much to be desired, and so car rental is probably the best option., especially if you want to explore, and explore some more. There is always a site or view beckoning further on. Use caution on the interior's more remote mountain and village roads, though. If you do choose to rent a car, you would be wise to hire it before arriving for the best rates. 

There is no centralized bus system, but several private companies with various schedules. What are called "buses" are often actually mini-vans, though they are efficient. These buses travel along the main arteries, however, and do not travel to the interior.  Bus tours of the island are also available for those who want to see the sites, but not do the driving.

Riding a scooter around Corsica is another interesting option, as it affords an up-close-and-personal experience with the area, especially the coastal roads and beaches. Using a scooter in the city gets you around quicker than other local modes of transportation.  

For the best eye-filling travel, it is imperative that you experience a trip on the  Micheline or the Trinighellu, Corsica's "little" trains. These trains follow a sometimes fearful, yet visually awe-inspiring route through the mountains between Ajaccio and Bastia, but just about everywhere you go in Corsica, you are confronted by dramatic scenic beauty, so whether you drive, ride, or float, you won't be sorry.