Yup, Dexterity increases both accuracy and damage for ranged weapons. You can check this by howering over the damage number under the weapon slot in your inventory and it tells you which stats increase what and for how much.
As for the unique bow you've mentioned, it's Titanstring bow. I actually haven't checked that one in detail when I obtained it, but I believe it also primarily gains bonuses from Dexterity while Strength is merely used as bonus damage.