What a great idea! From Tiffany:
Have you seen those cute "bib clips" that are out on the market now? Really cute, and handy to be able to use any towel (or even restaurant napkin) as a bib. But they're a little pricey. Hack it with a sheet holder. Piece of elastic with "grabbies" on each end, made to put under the corner of your mattress and hold the sheet in place – availble everywhere, for a couple of bucks. And those extra prefold diapers and burp rags are great "bibs" with this method, too!