You can use flannel backed vinyl table cloths, clear vinyl yardage from Joanns or Hancocks or any other place that sells it.

Hancocks Fabrics has quite an assortment of thin plastic materials in different weights. They also have a few thin plastic table cloth fabrics in colors. These could be used to waterproof the back. I would spray adhese the bib fabric to stick it to the plastic, then stitch bias binding around the edge to complete the bib. Hope this helps.
Angel

new waterproof fabric in walmart!!!! called PUL. don't know why. it is for making baby things and is in bright colors! i just made 8 beanbags for my granddaughter as she wanted them waterproof. easy to sew and cut. very flexible.you could make the whole bib out of this stuff. lynne

The drapery lining that is used for "Blackout" linings has a rubberized backing. Not sure pricewise if this would be more economical or not but just have a look next time you are in Joannes or Hancocks.

If you don't find the PUL at Walmart, Joanne's has it. Can use your coupon for a cut. I only found white there, but that was ok as I use it for bib backs. It's not with the regular fabrics...but forgot where it is!!

Hancock Fabrics has a rubberized fabric called Baby Dry.I use it for the back of all Avery's bibs.You could also make changing pads out of it.(I need to make a large one for her now)It is reg priced at $10. yd but if you sign up at Hancock Fabrics they send you a sales flyer about once a month.It will have a 40% off coupon so you pay $6. and it is wide, maybe 60inches. It has rubber on one side, bonded to flannel on the other.Wash and dryable.-Toogie

When I made bibs for my dad (he had Alzheimer's) and would drip down the front, I used micro fleece on the back. The density of the fabric kept the moisture from his shirt and pants. I also used the front of a buttoned shirt so his "bib" looked like a shirt without sleeves. I thought it helped him keep is dignity and so did my siblings.

The PUL at walmart sounds great, however drapery lining is by far the most economical i think mine was 3.49 a yard. That day all utility fabrics were on sale, so it was further discounted.