You're right, damage charms are specific to melee weapons; I never really paid attention to the description before (aside from the relatively low damage amount), and didn't use any charms.
I've put a normal damage enchantment on pretty much every bow I've used with an enchantment slot, though, and it does increase the ranged damage.
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I must have missed something on my enchanting choices so I will go back and change my enchantment.
I may have misunderstood normal damage and thought normal damage for melee. Who knows ..

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Kel******