Joanns carries several thicknesses of clear vinyl. The one with the blue paper is very thin ($2.99 per yard at 54" wide). I use this whenever I make bibs (between the layers of fabric), make-up bags and lining the pockets of diaper bags. I just use a longer stitch and sew a bit slower. If it is an area that will be stressed, I use a bit of stitch witchery inside the seam and when I iron it, it 'plugs' the stitch line. I have found this thinner vinyl washes well and have not had problems with the baby bibs.