I did that journey 5 or 6 years ago twice in 10 days. No hotel shuttle and had to take a taxi.
The first time the taxi driver grumbled, the second time the meter read over double the charge of the first time. Even intervention by the hotel staff didn't change his mind that I needed to pay what was on the meter, but there was a lot of arm waving and winking going on.
So, in my experience, take a taxi but check that the meter is set to zero before you set off