I'm into traditional archery, but only bow-hunt every couple-three years or less, and usually only deer when I do. (sometimes turkey) I do shoot often, because it's so good for the body, heart and soul, eye and hand/body coordination, and range estimation. However, I think a musket out-ranges a bow, period. (in hunting situations, military applications are a whole other story) There are exceptions, but the bow has a much greater pronounced trajectory, and that makes range estimation more critical. Another thing, there's more movement with shooting the bow, which can spook game, and game will also "jump the string", meaning they will duck or jump at the sound of the arrow being released. Very little movement pulling a trigger, and a ball flies much faster than an arrow. The bow is a good weapon in experienced hands, and I believe many stuck with the bow, and preferred it even after the introduction of the musket, but I think the musket does give one more "practical" range, and kills more quickly.
The bows used "back in the day", (same as the bows I shoot) were also not well suited to being left strung for long periods of time. Muskets can be left loaded for....wait for it....long periods of time.
After rifles became common, and the trade with Indians for deer hides was going strong, it would not make sense to harvest deer with a bow and limit your shots to close range, when a rifle would take a deer easy at 100 yards, and the Natives and Long hunters alike could shoot well out to 200 yards. I think that was probably the period that Native people switched to the gun, or rifle, more-quickly. The earlier "switch" probably occurred due to the British and French supplying them with muskets for military purposes. But even back then, there was a Indian/Native demand for fowlers, for hunting.
However, even in the late 1800's many tribes at war with the white man were not using guns exclusively. I know the Apache relied on the bow up until the very end. In fact, you will see many pics of Indians with a bow and arrow quiver on their backs, but armed with a rifle.