An Etymological Dictionary of the German Language/Annotated/Bauer
Bauer (1.), neuter and masculine, ‘birdcage,’ a word foreign to the Upper German dialects, from Middle High German bûr, used only in the sense of ‘sojourn, birdcage;’ but Old High German bûr has the further meaning of ‘house, chamber.’ Anglo-Saxon bûr, ‘dwelling’ (to which English neighbour from Anglo-Saxon neahgebur is related; similarly the more general meaning of Bauer appears in High German Nachbar), English bower, with which English dialectic bire (‘cowhouse’), Anglo-Saxon bŷre, is connected. The pre-Teutonic form would be bhûró, with ro as a derivative suffix. See the three following words.
Bauer (2.), masculine, in Erbauer, Ackerbauer, ‘tiller,’ from Middle High German bûwœre, Old High German bûâri (Gothic *bauareis is wanting), the term for the agent, from bauen.
Bauer (3.), masculine, ‘rustic, peasant,’ historically and etymologically different from Bauer (2.), for the Middle High German form is gebûr, Old High German gibûro, masculine, which belongs to the Old Teutonic bûr, ‘dwelling,’ discussed under Bauer (1.), and means literally ‘co-dweller, joint-occupier,’ then ‘neighbour, fellow-citizen’ (compare Geselle, ‘one who shares the same room’), and at a later period ‘fellow-villager, peasant, boor.’ See also Nachbar.