score:11
Yes, bows have been used to fight a duel, according to this
...seems to have occurred in 1791 when two gentlemen fought a duel with bows and arrows at Edinburgh shooting three arrows each without damaging each other
from the book Archery. It doesn't mention how much alcohol had been consumed first (brings back images from Highlander)...
Tracing the references ends with Scottish journal of topography, antiquities, traditions, etc. etc. etc., vol. I, 1847, p. 96:
So the event occurred on the 10th of February of 1791, in the Meadows, Edinburgh, with seconds. Hence a proper duel. The report is of an event from half a century earlier -- perhaps the newspapers of the day reveal more details!
Upvote:2
Negativa non sunt probanda. If really bow duelling never occurs, it is very hard to find out an inherent evidence.
In my knowledge of Italian crime law, the more lightly punished "delitti cavallereschi" (crime law offenses related to cavalry customs, and so somehow perceived as less heavy) were possible only if duellers had used specified "cavalry-fair weapons", which surely didn't include bows.
Upvote:2
The point of a duel is to defend one's reputation against an insufferable insult. The duel demonstrates that the individuals in question are gentlemen with courage and conviction and that each values his reputation more than his life.
Swords and pistols serve that purpose very well. Both effectively require that one face one's opponent and demonstrate courage. Each party (and their seconds) can see that the other stands firm and does blink or flinch.
Bows don't provide that; I suppose it is possible to use a bow at a range close enough to see whether the opponent blinks, but if you are at that range, then swords or pistols are a better choice.
In comments above, we got drawn off into a side discussion of whether bows were used by the nobility; while there were cases where nobles used bows, I'd wager the bow was never the weapon of choice for a noble. The defining weapon of the noble class is the sword, and if the goal is to demonstrate one's right to the title of gentleman, then the logical weapon is the sword. [A much longer answer would justify that assertion, and discuss the role of the lance and the pistol; I'm going to leave that to someone else to document]
As @Filipof says, it is impossible to prove a negative, but I'd be very surprised to discover a duel fought with a bow.