Tricia at Made By Me & Shared With You shares a free pattern for this baby bandana dribble bib. They’re made from two layers of fabric. She suggests a flannel for the top (especially cute when done out of a bandana print flannel), and a flannel, fleece, or terry cloth for the bottom. For a closure, she uses a buttonhole at one end of the bandana. There is no button; the other end of the bandana slides through the buttonhole and fits snugly enough to hold it in place. Go to her blog for the pattern and a tutorial showing how to make them.
[photo from Made By Me & Shared With You]