Bordeaux has an international airport (Bordeaux-Mérignac Airport) (code: BOD). Flights are mainly domestic but direct flights to some major European cities or "hub" airports (Amsterdam, Barcelona, Lisbon, London, Madrid, Rome, and others) exist. During the summer months, more direct flight options are available. A complete list of destinations can be found here.
Traveling from oversees will generally require changing air planes (likely via Paris Charles de Gaulle (Roissy, CDG) airport). During the summer months, Air Transat offers two direct flights per week from/to Montreal (Wed and Fri).
Main airline serving Bordeaux is Air France (or its low cost company Hop!). Other airlines serving Bordeaux include Air Transat, Aerlingus, British Airways, EasyJet, FlyBe, Iberia, KLM, Ryanair, Volotea, Vueling, and others. A complete list can be found here.
A regular bus (line 1) runs every 20-30 minutes to the city center (1.40€). The bus stop is just outside the main arrival terminal. There is also an Express bus (Jet Bus) that runs every 45 minutes and connects the airport with the train station (fare about 10€).
For coming from the airport : bus 1 to Quinconces, stop Lycées de Mérignac, then tram A to La Gardette ou Floirac Dravemont, stop hôtel de ville.
The Taxi stand is just outside the main arrival terminal. Taxi fees to Bordeaux are (depending on the time of arrival) between 30 and 40 Euros. The driver may add some additional fee at the end for luggage.