At Ngurah Rai International Airport (also called Denpasar International Airport), you can book a car and a driver to take you to Ubud. There are several different companies to choose among, but make sure you choose one of the official companies, so you don’t get scammed. It costs approx. 400000IDR and takes about 1.5 hours, depending on traffic and time of day.
A new Grab Lounge has also opened outside the airport. Here you can book transport through Grab, which is an app that works like Uber. The staff can help you set up the app and make a booking, and you can relax in the lounge while you wait for your driver to arrive. The prices are about the same regardless of where you book, but I personally prefer Grab, which I think is really convenient.
If you go with one of the car+driver companies, they sometimes recommend that you also book the return trip from Ubud to the airport immediately, and they will offer you a small discount. Though for some reason, my experience is, that the trip from Ubud to the airport is cheaper (if you book the return trip in Ubud), than the trip from the airport to Ubud, so you do not really save any money by booking the return trip in advance, and maybe you prefer choosing your own driver for the return trip after arriving in Ubud.
Some people recommend arranging transportation through the hotel you are staying at, but I’ve had very mixed experiences with that. If you are staying at a smaller guesthouse or a homestay, they can often get you a really good deal, but booking transportation through larger hotels is sometimes more expensive, than if you made the booking yourself, since the hotel often wants commission for sending customers to the driver.
Mini bus & Bus
While I am aware that you can book a seat in a minibus, I do not have any experience with going by bus or shuttle to Ubud from the airport. Considering the extra time it takes to pick everyone up/drop people off, and considering how cheap it is to go by car, I’ve never thought it was worth the effort. Though if you are on a tight budget, this is an obvious place to save. There is also bus service between Kuta and Ubud.
You can find bus time tables and search for local transportation here: