I'm not a native speaker, but I believe that this sense of "Bauer" is actually very rare in German (I can't find it in Duden online or pons.eu, for example). You'd be more likely to say "Erbauer", "Baumeister", or "Bauarbeiter". I would be interested to know what any passing native speakers think about this, though...
Here is the Duden link you missed:
It's rarely used on its own but you'll find it more often in compounds like "Brückenbauer".
BTW: There is a third (even rarer) meaning of the word: bird cage. I just learned of its existence 30s ago :)
"Bauer" is a totally normal word and as far as I know politically correct. It describes an occupation and I don't see any reasons why it should not be used.^^ I can't think of another word for it, either...when somebody uses the word "peasant" it would usually not be translated with "Bauer", even though that's it's actual meaning. Peasant carries an insult, that "Bauer" doesn't.