Bordeaux Airport is about 160km (100 miles) from Camping Le Vieux Port. Your best public transport route is as follows:
Take a taxi from the campsite to Dax railway station. (About 34km = 21 miles. One website is suggesting a fare of €84 for the journey). The staff at the Camping Le Vieux Port can probably help you find a taxi. Otherwise you can find some phone numbers here. (Click the blue buttons):
https://www.pagesjaunes.fr/annuaire/messanges-40/taxis
Take a direct train from Dax to Bordeaux Saint Jean station. (Journey time around 1½ hours):
https://www.sncf.com/en
Take the 30’Direct bus to the airport. (Journey time 30 minutes):
https://www.bordeaux.aeroport.fr/en/access-transport/direct-shuttle-airport-train-station
(Alternatively, take Bus Lianes 1:
https://www.bordeaux.aeroport.fr/en/access-transport/bus-lianes-1 )