If I want your opinion I'll beat it out of you - mind your own beeswax.
This came from the days when smallpox was a common disease that caused disfigurement. Those who survived the disease were left with pock marks on their body and face. Ladies would fill in the pock marks with beeswax. However when the weather was very warm the wax might melt. But it was not the thing to do for one lady to tell another that her makeup was melting.
Alternative: This may just be a childish rhyme to the phrase mind you own business. Biz is sometimes used as an abbreviation for business and rhymes with bees. Biz also sounds and is spelled similar to buzz, the sound usually attributed to bees.