I'm going off the lvl 10 bardic spell feature here, and my bard has bracers of archery and has been killing it when he's been using his bow.
The thing that makes me scratch my head about elemental weapon is that it deals 1d4 damage when the weapon hits. Note that it does not state that the ammunition becomes magical, just that it deals extra damage on a hit.
So would arrows fired from a bow that has elemental weapon cast on it continue to deal 1d4 elemental dmg if my character was to then cast Swift Quiver?