Is it permitted for 1 female passenger to ride with 1 male Uber driver after dark? The ride would be from the airport to hotel and only 10 minutes long.
It depends on the amount of traffic on the roads that will be traveled. If it is deserted at night, or at that time of the night then it is not permitted, however if there are cars on that road approximately every 10 minutes then it would not be yichud. This is regarding the halachic aspect of things, from a practical safety angle though you might want to consider some other way to get to where you need.
Toras Hayichud 4-4,6,14.