After being on this subreddit for a little bit I've seen plenty of questions about how Napoleon surely would have won at Waterloo if only he had some long-bowmen. After reading plenty of logical refutations I'm now convinced the the transition to guns made plenty of sense for warfare.
But what about hunting? When did the average hunters start switching to firearms, and did hunting with a bow completely die out and reemerge more recently or were there always people hunting with bows?
I can't speak to your question for hunting generally, but there is at least one specialized case in Native American history where the bow was preferred until repeating rifles: horse-mounted buffalo hunting. Check out this page, which discusses the advantages of bow and arrow compared to muzzleloaders: