Your best choice would be to look for local guest house in the wineyards. Type "chambre d'hote bordeaux" on google and you should find plenty. They are some marvelous ones and for the price of your hotel you would get MUCH better comfort and someting much more authentic

If you want to stay Downtown BX I would recommend the Hotel Le Normandie right in the center of the city next the the grand theater and the walking district.

Outside of Bordeaux you might want to check the Hotel "La Réserve" in Merignac (or Pessac at least at the border of the two). http://www.hotel-la-reserve.com/. They are mostly known for their restaurant but the hotel is quite nice apparently too. From what I heard though the rooms are all different so try to ask for a good one if you book with them or eventually book for a superior type of room vs standard. I think standard room use to be in the range of 60€ some years ago with a company rate. They do offer a ver nice garden and swiming pool. It is also convinient to acces to the Wineyard from there too