The only taxi service operating from the airport is the Ngurah Rai Aiport Taxi (+62 361 751 011, extension 1155). The rates are fixed so you don’t have to waste time negotiating. The fare works out cheaper if you can carpool with a couple of other travelers (up to 3 passengers per taxi). No other taxi service has a counter at the airport. You may get solicited by private taxis, but that can be a little risky so be careful.
You could also have the hotel send you a car to pick you up from the airport. You could also rent a car from one of the counters at the airport.