|Bamboo in diapers has some poly in it, so that may be the issue.
It's possible that your diapers have some poly, but certainly not all bamboo dipes have poly. You might call the manufacturer because while most do state 2% poly or whatever, it's not legally necessary to declare anything less than 5% on the label. Some manufacturers I know of use 0% poly fabrics, though, so certainly don't assume there has to be some.
I have no idea why your kids would react to bamboo. Maybe they're allergic to bamboo cellulose, or something else in those dipes is irritating them. It's a very interesting question. I wish I could answer it!