I've travelled there recently and may be of help.
Uber is a no-no in Bali. People still don't like Uber there. And the app doesn't really work there.
- Private Cabs
You can use Bluebird or Grab for cab bookings. Bluebird is a bit costlier than Grab. We have faced no issues with either of these cabs while travelling to places long distances as well, and we used these both services a LOT.
I found that both Grab and Bluebird don't service in some areas like Sukawati and Giyanyar (better to hire locals or rent bikes if you're planning to visit these areas). And would always suggest private drivers if your taking a full day tour (non-commercial, informative and friendly for long tours)
If you're heading to airport from Seminyak, Kuta, Ubud go for Grab or Bluebird
If you're heading to the airport from places further from these three, better hire a local driver (your hotel will have contacts with local drivers) or utilise the hotel's cabs.
Ubud, Seminyak and Kuta are quite serviceable and we were able to book a cab from Ubud to Airport immediately without any hassles in Bluebird
You can haggle with local drivers to reduce the price of the ride.
Most of the Grab/Bluebird drivers don't respond to cab bookings post 9 PM even though they are very close by. They do this to take people for private ride with increased cost.
A day ride with a local driver for 8 to 12 hours should cost you about 600000 Rupiah. They're cheaper and the drivers are more informed.