In the seventeenth century, bibs were introduced to protect men’s clothing from the consequences of their own bad table manners.
Women did the same, but their bibs were fancier and were made of lace or muslin with frills to frame their faces.
Because these bibs were tucked into the tops of low-cut dresses, they were called tuckers.
On special occasions both men and women brought their own bibs and tuckers to the banquet and, just like their clothing, these made a fashion statement.
That’s why we say that someone well dressed wore his or her best “bib and tucker”.