Bordeaux-Mérignac airport has a number of direct connections: bordeaux airport
There are regular buses to the city center (30-45 minutes).
A Taxi ride to/from the airport costs 30-40 € during the day, slightly more at night.
Trains stop at Bordeaux-Saint Jean station. The train station is 10 minutes from the city center by bus or tramway. For details about train schedules, see the SNCF website