Consider ordering a sample packet of mesh from Seattle Fabrics.
Scroll down to the bottom of the page.
There are two sample packs filled with meshes; you can either order one or the other for $2.00 each, or get both for $4.00
1 of 2 - Bag and Screening Mesh; includes: Dive Mesh, Fiberglass Screening, No-See-Um Mosquito Netting, Leno Mesh, Medium Polyester Mesh, Trampoline Mesh, Phifertex and Phifertex Plus.
2 of 2 - Clothing Mesh; includes: Athletic Mesh, Sports Mesh, Mini Mesh and Power Mesh.
I would think that the first sample pack would have in it what you need. The Phifertex or Phifertex Plus seems interesting for your application.
"I don’t think it needs to be stretchy, but should be comfortable."
As far as binding the edges I think that I would use the 1" #2036 lt wt - SOFT grosgrain from Quest Outfitters.
Scroll down about one fourth of the page. ;-)