Bordeaux has an excellent public transport system of busses and trams. Single rides cost € 1,50 (including the trip om Liane 1 from Airport to anywhere in city). A ticket is valid in connections made within an hour from starting. Cheap and comfortable is the 7-day pass with unlimited rides for € 13,00. You can buy this tickets from machines at tram stops and in front op airport hall B where Liane runs to the city every 10 minutes.
An alternative for public transport is the public bike system V3 (V Cub). A week pass which you buy with debit or creditcard at any of hundreds of bicycle parkings. Rides till 30 minutes are free, and 30 minutes is enough to get you from anywhere to anywhere, including Talence university campus.
Downtown Bordeaux is small enough to be explored on foot.