Bordeaux has plenty of hotels in all price ranges. As an indication, you can expect to find double or twin rooms in city centre in two star hotels for € 70 – 100.
Be careful: end of July is in the busy touristic season in Bordeaux. Don’t forget to book your accommodation early, or you might be left with much less choice and much higher prices.
Larger groups or families might be better of with an apartment which you rent through sites like Wimdu.
Close to the railway station you’ll find the youth hostel where dorm beds go for € 24