We booked a private transfer from Aqaba Port to Petra on 04/10/2023 using https://taxiaqabajordan.com/. After leaving a message there, we got contacted via WhatsApp +962 7 8555 8586 and all further communication was via WhatsApp. The operator always reacted very quickly. We had to send in copies of our passport due to Jordan law, which was also ok to do via WhatsApp. When we left the ship, we understood, since the authorities kept everyone's passports to be returned the following day to the stateroom.
We were 3 adults and paid 140JD for the whole taxi (Total, not per person). We were picked up right in front of the port terminal (visibility to the ship, maybe 150 m). The driver had a sign with our name on it. We then drove to Petra (about 2 hours), with a short coffee break (no extra charge). The driver waited for us on site for 3.5 hours and then drove us back to the ship. We paid the entrance fee for Petra ourselves at the counter in the visitor center. There is no need to reserve that in advance. Thanks to the driver's very good tip about paying in cash, we were able to get the cheap ticket for JD 50 per person instead of the more expensive one for JD 90 per person. The cheaper price normally applies to people who are not just day tourists and are staying in Jordan. But passing 3 50-JD bills gave us three tickets. That tip alone was worth its weight in gold. There is an ATM machine just outside the entrance to the Visitor Center in Petra that accepted VISA for a reasonable 4JD fee. In Petra we were always one step ahead of the cruise ship buses. The taxi was well maintained and big enough for me (2 meter tall and not exactly slim). The driver spoke quite good English and drove very safely. We would do the tour again at any time.