If you hit a creature with multiple missiles (which occur simultaneously and therefor use only one damage roll by the simultaneous damage rule), would you add the bonus to the damage taken to the chosen creature as part of the damage roll for those missiles and thus multiply by the number of missiles or after the damage roll and only add the Bardic Inspiration die once?
If a creature has a Bardic Inspiration die from you and casts a spell that restores hit points or deals damage, the creature can roll that die and choose a target affected by the spell. Add the number rolled as a bonus to the hit points regained or the damage dealt. The Bardic Inspiration die is then lost.
The Magic Missile spell (PHB p. 257)
You create three glowing darts of magical force. Each dart hits a creature of your choice that you can see within range. A dart deals 1d4 + 1 force damage to its target. The darts all strike simultaneously, and you can direct them to hit one creature or several.
The "Damage Rolls" section of the rules (PHB p. 196)
If a spell or other effect deals damage to more than one target at the same time, roll the damage once for all of them.