Now, a bonus action is a noticeable cost.
Perhaps the AC bonus is always on, and you can use a bonus action to also gain +X elemental damage on each attack before the start of your next turn. I’d prefer a trade off.
I’m not sure it’s valid to ignore the utility of not needing a shield, and being able to choose an elemental damage type.
So, while wielding a weapon in one hand, and either an arcane focus, material spell component, or nothing in the other hand, you have a +2 bonus to AC, and you can use a bonus action to add your Intelligence mod to damage, and make your attacks deal one of Acid, Fire, Cold, Lightning, or Thunder, damage, until the start of your next turn.
That more damage per round than dueling, but requires a bonus action to do it. I’d also be fine with keeping the damage the same as dueling, because not needing a shield for the AC and choosing damage type are both decent benefits.