That fabric patterning looks like Toile fabric which has been used frequently for chair coverings and curtains in earlier times. Now, if it is 100% cotton and lightweight, people use it like any quilt fabric. Is your Bark fabric more sturdy than quilting cotton? Then it may have been upholstery fabric. Here are some images from a Bing search.
https://www.bing.com/images/search?q...cw=1117&ch=623