Are you glueing the burlap to cardboard or something to stiffen it or are you just using the burlap alone? In my experience there are different firmness levels to burlap and I want the right image in my head (though I'm no fabric expert by any means).
I'd imagine midge lodge or glue would work, if your using a cardboard support then whatever adhesive you might be using should work. If you're up for sewing, a zigzag stitch along the last weft thread (think that's the right word) should give a different look with no fancy skills needed. Run the pieces through a machine in a row so it looks like bunting then cut the pieces apart.
The burlap ribbon is heavily, heavily starched. It holds its shape on its own without wrinkles . (For now- i imagine over time they will go limp). The weave is more open than I'd like, but as long as I baby them a little (use a pin for each earring so the pin rather than the fabric is the real support, etc), they should look fantastic and hold up well.
No sewing for me. I'm too lazy, the project is unworthy of that kind of time, and I'm not even sure I still own a sewing machine.
Worst cast scenario I know I can buy liquid seam stuff- it's just that it's expensive, I don't happen to have it on hand, and that stuff smells suspiciously like Elmer's glue. Since Mod Podge also smells suspiciously like Elmer's, and it's cheap, and I have a ton on hand- kinda hoping that'd work. Hmmmm.... wonder about going over the whole thing with Mod Podge to stiffen it even more.... (thinking "out loud" now....)