I was needing more bibs for our very drooly newborn and mentioned this to my husband.  He said the dreaded words, "Why don't you knit some?"  Now I've been challenged!  This is what I came up with after a lot of trial and error.
 
I love these bibs!  I can't get enough of them. Purl rows catch anything that tries to escape down the front.  Super easy pattern and fun to do.
 
Size:  Fits sizes newborn through 18 months.
Needles:  16" circular needles US 6 and 8, or use the magic loop method with 40" circular needles.
Yarn suggestion, listed in order of effectiveness all in worsted weight.
1. Superwash wool, the best! You can just throw it in with the wash and wool does not wick so it keeps the baby from getting slobber drenched. 
2. Acrylic.  Much better than cotton, not quite as good as wool.
3. Cotton isn't horrible, but I don't recommend it.  Cotton while absorbant, wicks so it will get baby's shirt wet.  It is also cold when it is wet unlike wool.
 
A link to the PDF file will be emailed to you upon completion of payment.