Find out in advance where the bride has her linen registry. Then have everyone bring a linens item. Everything from sachets for the linen closet, to White Linen perfume, to Queen-sized flannel sheets would be welcome. You and your guests might like to cross-stitch or even fabric paint some dish towels together as a project.
Send the guests home with potpourri sachets. The perfect invitations would be little 1” × 2” pillows you made yourself out of fabric snippets, scraps of lace, and fiberfill. Short of that, how about cutting out bed shapes from cardboard and hot gluing to them a tiny fabric bedspread you have to lift to read the invitation?