As far as I know, the earliest firearms took ages to reload, were less than accurate, and were plagued by a number of other problems that the bow did not suffer from. What was the advantage of switching to guns?
Firstly I'd recommend my post on the question When were pikes "phased out" on the European battlefield? What lead to this change? which discusses the rise of the musket.
As for your question specifically I will recommend /u/Rittermeister's post here on specifically this topic.
The basic reasons?
The English Longbow was an outlier of effectiveness but we can use it in the 'best case' scenario. With a 150 pound draw using a 905 grain arrowtip firing at about 250 ft/s that generates about 127 ft/lb's of energy with a firing distance of ~200 meters. A .69 and .75 caliber smoothbore musket can, with a 220 grain load, for the cost of half the range, achieve a muzzle velocity of ~1100ft/s and a kinetic impact of ~900ft/lb's. As in, a gun gets to the target effectively instantly and penetrates just about every single thing they're wearing. If by some miracle they survive they're knocked onto their butts and aren't getting up. However the rest of Europe did not use the English longbow and the rest of Europe reports during the crusades, as /u/Rittermeister says above, that padded mail would stop a hail of arrows in their place. They simply did not have penetrating power. In other words when an arrow hit someone it might kill them; when a bullet hits someone it will kill them.
Training. Bows required years of training to become mildly proficient at; even if we're just talking about 'volley fire' they required arm strength and training to use to a significant way. I mean the Longbow is the commonly cited example and it had a 150 pound draw weight up to 185 pound draw. It frankly required a certain level of physical aptitude to use a bow. A gun required none of that, anyone could use a gun. Further a gun required, at most, 1-2 weeks to train a man to use. It didn't require years of training and physical aptitude it required pointing at the enemy and pressing a button.
Morale. Being shot by a musket is fucking terrifying. They blow out ear drums, they produce a crap ton of smoke, and they penetrate just about everything coming your way. Now that's just one -- imagine 100, or 200. All coming at once with all the smoke and sound. Bows produced a similar effect from volley fire but nothing like the boom and the smoke of a musket and that can't be ignored. Dave Grossman's On Killing talks about this specifically and points to it being the crucible point to why, despite being 'technically' less accurate and having less range than bows early muskets took over.
Let me emphasize this again: Firing a bow is a very physical activity. Even a sick, weak, and old person could use a gun where using a bow required top physical shape, years of training, and even then they will reduce in effectiveness as the bowman himself wears out.
Ease of production. Muskets allowed anyone to use them and, believe it or not, were even easier to produce. Yes it required more mechanical parts but they were consistently made mechanical parts --- the parts were common amongst all of them and it was almost 'standardized'. Bows required finesse to make and craftsmanship and perfect wood and flax and all that bullcrap. A musket could be made by any self respecting blacksmith in a relatively straight forward fashion and in larger amounts and a longbow required 4-6 required to make! If a musket was broken it was standardized parts so it can be fixed and reused relatively simply; if a bow was broken it was done for.
They did not take that long to reload! Matchlock muskets could fire 2 shots per minute reliably and when we got to flintlock muskets in the early 1600's that time was reduced to a 15-25 second reload time -- up to 4 shots per minute. They also were not 'horribly inaccurate' and could be reliably fired up to a range of 75-100 yards. That is not bad at all.
The simplest fact of them all: Armies equipped with firearms consistently defeated those without them. Do we need another reason than that?
So the tl;dr: They replaced a weapon with significant range but with lesser penetrating power, high training burdens, high manufacturing burdens with variable quality and less flexibility for a weapon with less range but significantly more penetrating power, no training burden, next to no manufacturing burden with consistent quality and shared parts with more flexibility and the added affect of being freaking terrifying.