Kitchenstitchen
The fusible laminate needs to be certified lead and Phthalate free. The cotton and the binding are exempt on your bibs. Contact the manufacturer of the laminate and see if they have tested it for lead content and phthalates. If they have not, then you have a choice. Find a tested vinyl where you can get the testing information, have it tested yourself by a cpsc certified lab, or change your design and not use the laminate.
Check with Michael Miller fabrics, I think they were going to issue some of their fabrics with approved/tested vinyl coatings.