("It", of course, means the sting, not the bee!)
This is a very old Japanese folk remedy on the basis that the ammonia contained in urine neutralises the venom in the sting.
Peeing on a sting must be especially difficult if it's on the back of your neck, or quite a desperate measure if the sting is on your face. But it's pointless to do anyway.
Nothing you put on your skin can neutralize or counteract the venom of a bee (or wasp), because the venom is injected too deep into the skin.
Bee venom consists mainly of melittin, apamin, MCD peptide, histamine, hyaluronidase and phospholipase-A2. Urine is mostly water, with a bit of urea, chloride, sodium, potassium, creatinine and other dissolved ions, and inorganic and organic compounds.
Urine does not neutralise bee venom.