Mine is the dribbler from 'Nam (still is) and had reflux so was mighty spilly too.  I found the Silly Billyz bibs still got soaked through, and the only ones that work on her are rubber-backed ones (the rubber is melted on to the back of the fabric, so it's not 2 separate layers like most bibs - you'll know what I mean if you see them, those rather cheap bibs in the warehouse are the best!).  Look for white rubber backing, and towelling-like fabric on the front (it tends to absorb stuff really quickly, rather than let it run down the bib like I found a lot of others did).  With Ella, I use bibs with ties instead of velcro, as I can tie them up to sit quite snugly on her to stop everything running under the bib, so that keeps her chest dry.  Now I only bother buying the Warehouse ones - they're just over $1 each and work really well!  And the backing on them doesn't eventually rip up in the wash like plastic backing tends to do over time.