To make the bib, trace a simple bib pattern on a newspaper. You can trace from a bib that you already have if you like. You can use a lightweight broadcloth for the top piece and a soft terry cloth for the bottom. Bath towels work great in lieu of terry cloth; and they come in more interesting colors too. Sew the two pieces of fabric (wrong sides facing out) together, leaving a little two inch opening to turn right side out. Once you've turned the fabric right side out, iron flat, then top stitch around the edges. (Make sure that the fabric on the two "arms" of the bib that snap around baby's neck are wide enough; if you make the fabric pieces too skinny, you'll have a bugger of a time turning them right side out after you sew them.) Then you can put little snaps to finish off the bib. (You can find a little snap kit at Walmart.) Snaps work much better than velcro; they don't stick to or snag other clothing items in the wash.
These make great baby shower gifts. They are also a great way to use crazy fabrics that you wouldn't dare sew into a shirt or a skirt.