I can't answer specifically, but I can tell you that you've wandered in to an etymological clusterfuck. There are many words for singers, musicians and poets from the middle ages, and they're pretty much bound to nationalities. A bard was originally not a musician, but a poet. This meaning has been changed by romantic popular culture afterwards.

If we're talking about people travelling (and performing in I assume) from inn to inn, wandering minstrels or troubadours fit the description better. The original bards had patrons, although this could also be the case for minstrels and troubadours I guess.

Inns in general were far from as common as fiction might lead us to believe. We often overestimate the level of urbanisation that existed in the middle ages, and the closest thing you might find to an inn outside of major cities was a farmer offering you a place on his farm to spend the night. So to answer the question directly, they definitely weren't as common as we might believe.

If you include the Viking age in your definition of medieval times, poetry was an essential part of Norse culture. While Scandinavia consisted of largely rural petty kingdoms at the time, which made travelling around as a professional bard pretty impractical, every jarl with respect for himself had a Skald in his court. Skalds were poets primarily, but they may very well have accompanied their verses with a musical instrument like a harp.