Scotchguard spray and a heavy dose of laundry starch might help. Eventually the 'best' bibs were reserved for important events and the others for use in the house where no one could see the stains.
Next thought, you could enclose the bib in a plastic paper saver with the opening on the bottom so that nothing can drip in, but still starch the heck out of it because all it takes is one drip to make a mess.
Sounds like you need a bib for your bib! Hum, I understand that even tho my kids haven't worn bibs for a while. I had some nicer ones that I just hated for them to be ruined with stains. Perhaps tape a piece of plastic wrap over the cross stitched area?
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