I've been looking over the way my streight bow tie is constructed.

As far as I can tell, it is made from a single strip of fabric that is cut parallel to the grain (not on the bias); folded in half along the length; then seamed along the open edge and the ends.

It is, of course, then turned outside in. And like I said before, the middle part that is around the neck is folded over itself in a couple of twists and sewn down.

I think I can reproduce that in any number of materiels.

I tride an experiment and took a strip of cotton material that was folded in half (not sewn), and was able to tie a bow that was all right. So I'm thinking I could probably do this with the right streight edge and a bit of careful sewing...