This is tricky...
I think it says somewhere that forced movement doesn't cause OA. Is this forced movement for this purpose?
OTOH "You also don’t provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction." Why specifying it if it's not important? And yet I seem to remember that Mearls said that the intention was in general to make it not possible to "force provoking an OA".
Honestly, in this case I would rule that the Bard doesn't get an OA.