Updated: May 6, 2019
If you want to book a Grab or Go-jek right from the airport you can purchase a SIM card within the airport. The prices are pretty much the same as on the island. The most common providers are SimPATI and XL.
I recommend to buy XL because it allows Netflix and it has a quite good coverage.
You can buy them with different data packages. If you use it for random local calls, a bit of navigation in google maps for one week you are very well off with 1-2 GB. If you want to use it for heavy internet searches and Netflix a 5 GB for the start would be sufficient. You can recharge them along the roads nearly everywhere in Bali.
Let the shopkeeper install your SIM card and get it activated. All promts will be in Bahasa Indonesia, so if you don't speak the language you will have difficulty to activate yourself.
A indicator for prices are around 70.000 IDR for 5 GB XL card.