Bottle-feeding Mamas

How in the world do you keep your babies dry?  Unless I strip mine down to their diaper, their onesie ALWAYS gets soaked!  They're messy eaters, and no matter what I try I'm constantly having to change them.  Mind you it's not because they're "dirty", but because I won't let them sit in wet clothing.  I use two bibs, burp cloths, drape them all up and to no avail.  So please share your secrets!!