1

Taxis are cheap enough for all of your proposed travel needs.
On my last visit, August of this year, I hired a taxi and driver for USD20 for 10 hours. In that time we drove from Seminyak to Singaraja and back, with tourist stops in between.

Therefore Airport to Hotel should be easy. But you will need to bargain for the price. You wll be told that there are agreed fares for the trip. That is true to a certain extent, but you can still do some bargaining.

The above will be a guide to what you could get the trip for. PS it is about 3.5 hours in the taxi one way. As the driver will come back alone you will not be able to get a one way fare. You will also pay a premium from the airport.

Same in reverse for your trip to Ubud.

Do not get upset about being "ripped off", work out how much a taxi at your home location costs. I cannot get to the airport from home for less than $25, a distance of about 5km for me.

2

Waka Shorea is at the westernmost part of Bali, near with the harbor. If you mean Denpasar is from Center of Denpasar, it will take 4 hours (if your driver fast enough). But if you mean Denpasar is from the airport, it will take 5 hours (but usually more than 5 hours), because the airport actually is in Kuta.
If from Denpasar City, yes it will cost you about USD 20 (depend on what car you used). But if from airport will cost you USD 30 until USD 40 to your hotel.

3

"On my last visit, August of this year, I hired a taxi and driver for USD20 for 10 hours. In that time we drove from Seminyak to Singaraja and back, with tourist stops in between."

Fifteen years of full time living on Bali and I've never heard of such a deal!

Have you got that driver's name and hand phone number please?

A realistic rate for a private Balinese driver for 10 hours is around 600K IDR including gas. US $20 would hardly cover the cost of gas for a round trip ride, Seminyak to Singaraja and back again.