Sure you can make them without bias tape,but if you want a loop by which to hang them up,you have to remember to insert it before sewing it completely up.Layer the pieces like this.Your filler piece,the backing,rightside up,your hanger strip folded in half and with the majority of it hanging towards the center,then your top piece faced wrong side up.Start sewing about an inch or two before your hanger,so that insures that it will be caught up in the sewing.Sew most of the way around leaving an opening to turn it right side out,smooth out,press if needed.Then either hand stitch the opening closed or fold it in and top stitch all the way around.
Hope this makes sense,as i'm not very good at writing directions.
Kathi