I want to get to Denpasar from Gilimanuk (Bali, Indonesia)
What transportation options are there available (buses, shared taxi, taxi, or else)?
Note that I do NOT have my own car.
There are frequent buses from the bus depot in Gilimanuk to the Ubung terminal in Denpasar.
The bus depot is very close to the ferry terminal. It should be no problem to find a bus to Denpasar especially after the arrival of a ferry.
The price is 40'000 IDR per person.
I'm sure you can get a taxi as well, but that will be much more expensive.
You can ride a scooter direct; give yourself a full day to do the trip. The road is reasonable but busy with traffic, trucks hauling cargo between Bali and Java. Also, arm yourself with a valid international drivers licence when riding around Bali to fortify against the inevitable Bali style traffic fines. It is quite a nice ride.