On one hand, twill tape would do the job, but the real question is, "What is considered safe?" for such a thing in this day and age.
Is the tape simply long enough to have velcro applied to both ends so that overlapping the tape ends will hold the bib in place? Actually using bias tape or twill tape to tie the bibs on would seem a potential choking hazard.
Now days, all those cute nursery sets so popular in the 80's are completely taboo as they are seen as death traps.
I'd research acceptable closures for bibs, just to be safe.