At the very base level, yes WoW classes come from D&D, after decades of getting the "Warcraft treatment" and becoming decidingly Warcraft classes. A Warcraft Paladin for example is heavily steeped in WC lore, to the point where you can tell a Warcraft Paladin from a Paladin in other games. Then you have wholly original Warcraft concepts like the Demon Hunter, which is distinguished by its Warglaives and half-demon/half elf appearance. Again, a Warcraft Demon Hunter is completely different from a Diablo Demon Hunter. The Warcraft Tinker as well has very unique attributes that have actually began filtering into other games because it works extremely well for a tech based class. However, you would never confuse a Warcraft Tinker for tech classes in Torchlight, Final Fantasy Online, Ragnarok Online, Guild Wars, etc.
Which brings us to the Bard.... Where is it in Warcraft outside of random NPCs in Order halls or disparate NPCs that happen to have a "musical" ability?
Take the "Bard" that Ielenia likes to bring up; "Hearthsinger Forresten". Here is his lore;
That's it. His abilities are a Hunter ability, a Warrior ability, and a spell that puts people to sleep.
Yeah, let's base a class on that guy.
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None with any significant lore beyond a paragraph. I suppose there's Lorewalker Cho, but I'd hesitate to call him a Bard. At least in the sense that someone could base a recognizable class upon.