I have two plants that have bullardiana as the name. One has light pink flowers with darker midstripe, the other which bears the epithet albiflora has not yet flowered for me. Neither have field data. However a very well known Mammillaria expert tells me he doesn't believe that what is in circulation as bullardiana is actually correct, and are just forms of hutchisoniana. He believes that bullardiana is actually a separate species and is geographically seperste from the main hutchisoniana populations. I await further information, but I don't think it will be son.