Why does having sex with mulitpal partners give you BV (bactrial vaginouise)?

Exposure. The more "partners" one has; the more exposure one takes on...Which potentially changes the normal flora in one's own body. Always have you(or your partner) wear a condom which can reduce this risk; and this is an easily treatable condition so see your health care provider if this has occurred.
It's a mystery. In many ways BV behaves like an STD, and like all STDs, the risk is correlated with frequency of exposure, no. of partners, etc. Among lesbian partners, it's definitely sexually transmitted. However, no sexually transmitted germ has been found, male partners have no symptoms, and treating male partner of infected women apparently makes no difference in risk of recurrence. Research continues.