I interpreted the phrase "which way the wind is blowing" to mean the prevailing fashion and majority opinion, so that the quote would contrast making decisions based on principled conviction with bowing down to momentary fashion and popular pressure. 

This is a major meaning of it in English as I know it. And I have a reference - see below. 

(This phrase, i.e. its literal translation, is commonly used in this sense in my native language.) 

Not surprising - they probably have a common historical origin, with somebody along the line translating the phrase.

However, looking it up, now I see that this is not its usual meaning in English, though such meaning is attested to some degree.

Whatever reference you consulted seems to have misled you. Here is a reference which explains:

The figurative sense of 'the way the wind blows', i.e. meaning the tide of opinion, was in use by the early 19th century. In November 1819...

So this meaning has been active for almost two centuries, if not longer. And since Bush is a politician, who ultimately succeeds or fails on the basis of the tide of opinion, this creates a strong presumption in favor of this meaning. If Bush were speaking as a sailor, it would be the other way around. But he wasn't.