Given the pop cultural timing of this, one may fairly assume that this take on bards is inspired by The Witcher, and the bard Dandelion / Jaskier (depending on what version of the stories you're familiar with). I say this is fair because the liberties the bard takes with his stories of the main protagonists adventures are a recurring thing, as are the points of why such liberties are taken.
(I've thus far enjoyed the books more than the show, but that's neither here nor there).
The truth, however, is that my fascination with the idea of a bard following a hero around for stories to tell goes way back to my childhood, and was inspired not by The Witcher, but by another classic of medieval fiction:
Monty Python And The Holy Grail.
Now, Sir Robin's minstrels aren't exactly 1:1 with Dandelion, but in the same stories Racnar (now Ragnar) came from was a bard who wanted to follow the hero around and tell of his adventures. I may or may not have actually referred to him as a bard, though it's possible? I can't recall. If I did, it was probably because there was a bard character in Final Fantasy IV (there was a rich tapestry of nerdy inspiration).
Either way, his role was the same, and it's now amusing to me just how similar he was to Dandelion, whom I only learned of after watching a bit of the Netflix series.
While it's possible I'm forgetting some other inspiration, I can't recall anything other than Monty Python that could have inspired such a character, so I assume I am recalling that correctly.