Firearms in the time period that is being aimed for were utter crap. It was well into the 1600's before guns began to out do bows and into the 1700's before bows were rendered completely useless by the introduction of rifles, which meant that guns could finally be relied on to actually hit the target
There were several reasons that, in spite of being inferior killing weapons, firearms were adopted. Firstly nearly anyone can pick up and fire a gun while it takes years to train an archer and develop the correct upper body strength for them to be good enough to fight in a war. For instance, English men were required by law to do two hours longbow practice every Sunday. It led to them having odd muscle proportions, their upper body strength being disproportionate to their lower body strength (drawing and firing a long bow, one of the few bow types capable of piercing plate armour, takes a lot of strength.)
Secondly, a volley of gunfire is more terrifying and thus a larger effect on morale than arrows. In this time period, warfare wasn't so much about actually killing the other side as it was seeing which side runs away first. 
Thirdly (this applies more to the later era than the current era though) you can attach a bayonet to a gun, which means you can also use it as a makeshift spear against cavalry. A bowman would have to carry a spear with him to achieve the same effect which just means more equipment to lug around.

Also, hello, this is a nice roleplay you got here. Lol.