Speaking as someone who has archery experience, it's a lot more skill oriented and has a lot more variance in field combat. The shots, while they can be quite fast, are not nearly as quick as a bullet. The skill with firearms tends to be with long range shooting. At short range, you can point and shoot and generally hit something. Even at 50m, a minimal amount of training is required to get to be accurate at that range especially with newer weaponry.

This may or may not factor in, I don't know, I'm not a history buff really, I know technology more than anything.

Personally I feel like the most contributing factor is that a bow is a comaritively fragile weapon. Most firearms are metal with wood grips. The core of the weapon is metal, and comfort aspects of it are wood.

Compare that to the requirements of a bow, where every part, aside from the riser (where the grip and sights are) needs to be flexible. The limbs, which are the upper and lower arms of the bow, need to bend and flex to provide the reaction force to fire the arrow, the string needs to be very flexible, but strong enough to handle the weight of the draw. Every part moves, bends and flexes as the weapon is drawn and fired. That flexibility introduces a lot of risk in terms of damage on a highly dynamic field of battle. At one time we had no alternative, and bows when weilded by trained archers, were a formidable force compared to the alternatives, which at the time were mainly knives, swords and shields.

The likelihood of a tool like a bow becoming damaged in the field (a limb breaking, a string breaking) whether through regular use, or intentionally by the enemy, or even by negligence, in stepping or sitting on the bow, is not trivial. Factor in that when a bow is at "rest" it's still under tension, and you can be hurt by the string or limb breaking unintentionally, especially if you're in the middle of a draw, and the difference is pretty clear in terms of operator safety. With a gun, whether a musket, rifle, or something else, generally you have fairly think iron or steel containing the discharge of the weapon. While misfires are still possible and the consequences of a misfire can be much more severe, they're far less common. I've seen people shatter arrows, sending fragments of the arrow shaft into their hand and requiring significant medical treatment; on a battle field, if you get a bad arrow that splinters when you try to fire it, which wouldn't be as uncommon as you'd like, then that Archer is out of combat for weeks or months. It's far less common for a firearm to have a similar catastrophic failure. Again, not impossible, just far less likely. It's far more likely to have a firearm jam or misfire in the sense that it fails to fire, than for it to fire in such a way that the operator is injured. There's small issues with the safety of an operator when it comes to firearms, beyond the obvious of shooting yourself, such as getting bitten by the slide (common on modern pistols), or impact injuries from not bracing properly for a weapons kickback. But given the limited amount of propellant in a bullet, it's far less likely to "blow up in your face" so to speak.

Given operator safety, and the relative ease of training (at least compared to archery), and the consistency of the performance of the weapon, operator error is effectively reduced to loading and aiming the weapon. The effects of operator errors is also reduced.

Factor that in with the lethality of firearms versus archery, and the accuracy, especially at long range, where an archer would need to factor in wind and gravity, at far closer range than a rifleman would, and the advantages are now far outweighing the negatives of firearms.

The benefits of archery is generally in the ability to reuse ammunition, the relative silence of the weapon, and the light weight nature of the materials used in archery. It's a good way to hunt and fight, but when it's compared to even (relatively) primative firearms, it doesn't really have the ability to compete. Most even better than average archers don't usually loose more than an arrow a second on a good day; once jacketed rounds became common and semi automatic rifles and firearms became commonplace, even a relatively poor rifleman can release more than one shot per second. So for shooting speed, either train for thousands of hours to become an expert archer, or pick up a revolver and squeeze the trigger as quickly as you can.

Firearms are simply better, easier machines to deliver projectiles down range in almost every comparison.

The Comanche were some of history's finest horse archers and it required the invention of the repeating rifle to end their supremacy of the plains.

There could have been a much stronger Spanish influence on the plains of North America had the Comanche not been there to turn their empire back.

You'll likely see bows and arrows in just about any movie that has Native American tribes as one of the belligerents.