The Bowyer, who is similar to an Archer, is a very straight forward class; there are no surprises or oddities. They are both foot solders carrying bows who can deal with enemies from a range without fear of counter attack (unless they are fighting another ranged unit who also has the Bowyer within their attack range). The main difference is that Bowyers are unable to use Ballistas.
Bowyers need cover and support. While they can attack sword or axe users without being counter attacked, any enemy in range can easily move in and fearlessly attack the Bowyer; not being able to counter attack at melee range is a small downside. Any type of ground unit, preferably one with at least moderate defense, will make for suitable cover. Remember, Bowyers are strong against flying units such as Pegasus Knights, drawing these enemies into your firing range will save you a lot of trouble later on.
Bowyers upgrade into the more powerful Ranger class. Upon promoting, you'll notice that they are unique as they can now use Earth magic as well as bows.