Originally Posted by carol45
but will the edges tend to stretch after the bag is sewn together?
Not if the bag is lined.
I do think the best idea is to foundation-piece on thin muslin. The muslin would provide additional stability to the pieced fabric. I would still cut the strips on the straight-of-grain.
The easiest seams are straight-of-grain to straight-of-grain. Sewing straight-of-grain to bias is much trickier. Sewing bias to bias is just about impossible unless you heavily starch the fabric before cutting so the fabric has no chance to stretch out of shape when you sew the seam.