Animalia is currently covered by a Taxonomic Framework that prevents me from helping you with this right now and only site staff (@loarie) can edit/move taxonomic orders. Currently, Adinetida is on iNaturalist, it just needs to be grafted to Bdelloidea. The same is true with Philodinavidae, though Philodinavida would have to be added. Hopefully this will get resolved soon.
iNaturalist currently uses the World Register of Marine Species as our external authority for most invertebrate taxa, but some portions of their tree are not as complete as others and it seems to be the case here. They don’t include Adinetida and Philodinavida (or any orders) under Bdelloidea. Are there any more robust and comprehensive taxonomies on rotifers we could potentially use an an authority?