Bordeaux is not California or anywhere else in the wine world where cheapest prices are found at source. In Bordeaux the châteaux do not sell their wine around the world, they sell it on exclusively to a specialised wine merchants based in the city of Bordeaux (négociants) who do all of their commercial work for them! To find the cheapest prices find a shop owned by one of them and dont buy generally at the château itself!
They buy the wines as a futures, before it has finished ageing in the barrel.
It is against the interests for the châteaux to sell the wine more cheaply at the château itself. In fact most do not sell wine at all to their visitors, if they do the prices are often more expensive than what a visitor could find in one of the shops in the city of Bordeaux (often owned by these same négociants). What is guaranteed is the provenance and a good range of vintages that you may not be able to find elsewhere (the château usually keeps a little stock of each year).
I use Joachim at La Cave Dourthe (one of Bordeauxs largest wine merchants) in St Emilion next to Grand Barrail hotel (beware of buying wine in the touristy medieval village of St Emilion – these are the MOST expensive prices around) for clients who have toured with me that wish to ship all of the world. The prices are 20% less than indicated as the French VAT can be taken off the price if the wines are destined outside of Europe. Often this saving pays for the cost of the shipping.
Some clients from Hong Kong recently purchased a number of very fine wines including Mouton and Yquem finding the prices compared more favorably with prices available in the Duty Free market of Hong KOng even taking the shipping costs into account. And the provenance and quality of the wine is for sure much less risky. Buying wines in Bordeaux from the wine merchants themselves you know that the wine has been bought ‘en primeur’ (futures) and never left the cool cellars until the day you ship them!