With nappies PUL is usually a hidden layer with either minky or polar fleece so it isn't against the skin. That kind of thing would work well for the bib too.

There is also the option of using a high end fleece such as malden mills which will prevent a lot of moisture from seeping through.

PUL should stop the moisture from getting through but it does get saturated eventually and will then leak. It's the tradeoff for a breathable barrier.

Where are you looking to get it from? There is some good cheap stuff available at bubbaearth for about $10 for a nice wide piece that yu will be able to get quite a lot from. It's cheap because it isn't fancy but good for a hidden layer. I have a bit here I can send you if you want to have a look at it first. PM me your address if you like