Do bees die after stinging once?

A honey bee's sting is barbed, rather like a fishing hook, and when the bee stings into animal (including human) flesh, the elastic skin closes around the sting preventing the bee from withdrawing it. When the bee pulls away the sting is left behind, together with the venom sac and the muscles that pump the venom. This causes severe injury to the bee, which dies from those injuries.

This is a bit of a cruel trick of evolution because insect stings really evolved to sting other insects. An insect's hard outer casing is its skeleton (called an exoskeleton) and when the bee stings another insect its sting creates a hole which doesn't close up so the bee can withdraw the sting with no problem and lives to sting again.

It is possible to be stung by a bee where maybe it doesn't penetrate fully and the bee is able to withdraw the sting. If this happens no harm comes to the bee.