To get from town to town in Bali, the best option is to take a private driver. They usually have large, comfortable cars with enough room for your luggage. The prices are also affordable, especially if you travel together and share the fare.
For travel in the city, the scooter is the preferred means of transport. Indeed, sometimes there are a lot of traffic jams in Bali and the scooter will allow you to go much faster than a car.
As far as prices are concerned, renting a scooter for a day cost about 50,000 to 70,000 rupees per day (3 to 5 euros). You can negotiate the price if you rent the scooter for several days.
The mobile applications to use are Grab or Gojek to get around. The drivers are very friendly, and these apps are reliable.