Hi Sherrie,
After at least an hour of searching, I'm sorry to say that we don't have any manufacturers for bibs or baby products in our directory. But I did find a company that was previously suggested by Frank aka fm123, ProjectAsia.com - They are like an agent that will help you find the right Chinese manufacturers for your product. I think this company will help you find a good manufacturer as opposed to searching on the net especially as you mentioned this is your first time :)
You can protect your design by applying for a design patent. I think this guide should help you understand how to apply for one and also has a link to guidelines that you need to comply with - Link hidden: Login to view
You might also find the tips in this thread helpful - Link hidden: Login to view
Hope this helps and good luck! Looking forward to your updates :)