There is no public transport on St Bartholomew's Island.
From the airport you can walk, take a taxi or rent a car to your destination.
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Rent a car
Travelling by car is best suited for longer stays. The island is very hilly and taxis may not be available in all areas.
There are counters for many car rental companies such as Hertz, Sixt, Avis and National right in the terminal.
As the rental companies here are small and have a limited number of cars, always book at least 3 months before your trip. In that case, you can also get fairly friendly rates from 300 eur for a week.
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Taxi
There are no known mobile taxi apps operating on the island, but there are always plenty of regular official taxis waiting outside the terminal.
Taxi fares from the airport to Gustavia are 15 eur and to the Cul-de-Sac resorts in the east of the island 25 eur.
On foot
If you're only visiting St Bartholomew's for the day, you're perfectly fine on your own two feet.
One of the most beautiful beaches, which also has planes taking off and sometimes landing over it, is only 600 metres from the airport along a footpath.
You have to walk for a while by road to the main town of Gustavia, but the shoulder is wide and safe enough and the distance is just under 2 km. The best way is to take the road at the roundabout on the left (route map on en.mapy.cz).