The description of the Wrathful Smite spell says (PHB, p. 289):
The next time you hit with a melee weapon attack during this spell's duration, your attack deals an extra 1d6 psychic damage. Additionally, if the target is a creature, it must make a Wisdom saving throw or be frightened of you until the spell ends. As an action, the creature can make a Wisdom check against your spell save DC to steel its resolve and end this spell.
You can expend one use of your Bardic Inspiration to cause the weapon to deal extra damage to the target you hit and to any other creature of your choice that you can see within 5 feet of you. The damage equals the number you roll on the Bardic Inspiration die.
So here is our Bard surrounded by enemies:
With a bonus action, he casts Wrathful Smite and then he attacks the Ogre. His attack hits the Ogre, so he grabs the Bardic Inspiration die to roll for Slashing Flourish; he rolls an 8 on the Bardic Inspiration die, so all creatures take 8 extra weapon damage.
- Does the sword hit all of them? (I assume yes.)
- Who gets psychic damage?
- Who makes Wisdom saving throws?
- Who is frightened?
Sidenote: The Battle Master fighter subclass has a Sweeping Attack maneuver, but its wording does not support the above interpretation of the rules. So no AE Wrathful Smite for the Battle Master.