Bv is bacterial vaginosis, an overgrowth of one of combination of gardnerella vaginalis, mobiluncus, bacteroides, and mycoplasma.
These are normal bacteria
for your vagina, but when a woman has bv, these bacteria grow in abnormal amounts. I don't think having oral sex
with someone who has BV would be all that appealing. But to answer your question, no you cannot get BV of the mouth.