The traffic in Denpassar will seem chaotic if you are a visitor unfamiliar with it, however, it seems to function with very little regulation. Since you are on holiday - spare yourself the trial and trust an experienced local driver instead. If you still do not want to depend on anyone else but yourself, we recommend a prior reservation with an official car rental service in Denpassar. We had good experience with Andreas Reich, also because he offers complete insurance cover with low cost sharing (andre-sewatama-bali.de; email@example.com). Around Amed there are only private car rentals that don't include any insurance, which might mean hidden financial risks.
In order to be mobile and independent around the villa, a scooter is the best option. It takes you along the coastal road at a comfortable speed, often making the road the destination. Rentals are available almost everywhere and also at the villa through Wayan who will deliver a scooter (or several) comfortably in front of the house.
Please note that an international driver's licence is required for driving a car or scooter.