"I am not sure if J.S.B. was inspired by it or stole it."

Actually, a bourée is not a specific piece of music, it's a dance form, like a minuet or a waltz. Composers such as Bach and umpteen others used standard dance forms as the basis for new compositions all the time (later, Johann Strauss, for example, made a career out of writing darned little but waltzes).

It was not at all uncommon for composers then and now to "borrow" themes from each other and change then or add their own licks to them. This was often acknowleged with titles such as "Variations on a Theme by (whoever)." Also, there were lots of well-known tunes floating around (often folk tunes) that nobody laid claim to, and composers would take these and play around with them.

Leonard Bernstein was criticized for his "There's a Place for Us" in West Side Story because it's a dead-ringer for a theme in one of Beethoven's piano concertos. Bernstein answered by pointing out that, historically, composers very frequently did this with no need to apologize to anyone, then said of the West Side Story song, "Of course I borrowed it from Beethoven. It's much too good a melody to be used only once." West Side Story was also a modern retelling of Romeo and Juliet.

The "folk process" is not limited to "the folk" (whoever they are).

It's only plagiarism if you take it note-for-note or word-for-word, making no changes, and then claim or imply that you wrote it.

Don Firth