Etymology
1. Inherited from Middle English bocchen (“to mend, patch up, repair”), of uncertain origin. Perhaps from Middle Dutch botsen, butsen, boetsen (“to repair, patch”) (Dutch botsen (“to strike, beat, knock together”)), related to Old High German bōzan (“to beat”), See beat; or perhaps from Old English bōtettan (“to improve, repair”), Old English bōtian (“to get better”). Compare botch. More at boot.
2. Perhaps from boggle.
3. Perhaps from botch (“patch, or a measurement of capacity equivalent to half a peck”). There is a hypothesis that bodges, defined as rough sacks of corn, closely resembled packages of finished goods the bodgers carried when they left the forest or workshop. Another hypothesis (dating from 1879) is that bodger was a corruption of badger, as similarly to the behaviour of a badger, the bodger dwelt in the woods and seldom emerged until evenings.
4. Other hypotheses include German Böttcher (“cooper (profession)”), a trade that uses similar tools), and similar Scandinavian words, such the Danish bødker. These words have similar origins to butt, as in water butt (“rain barrel”). Or possibly it may have been a derogatory term used by workers in furniture factories, referring to the men who worked in the woods that produced the “incomplete” chair parts. The factory workers would then take the output of that "bodged job" and turn it into a finished product.
5. The Oxford English Dictionary Supplement of 1972 has two definitions for bodger. One is a local dialect word from Buckinghamshire, for a chair leg turner. The other is Australian slang for bad workmanship. The etymology of the bodger and botcher (poor workmanship) are well recorded from Shakespeare onwards, and now the two terms are synonymous. See: Dutch '
botsen', Old High German 'bōzan'.