Of course you want to remove the stinger. You can apply a paste of baking soda and water to help draw out the toxins. An ice pack can help reduce the swelling. Monitor for swelling of the nose or mouth.
Wash it with vinegar, and bring your dog to the vet immediately.
You'll never know if your dog suffers an allergic reaction to the bee sting.
That could be fatal, especially so in young, sick and old dogs.
I took the pain of a wasp sting away on myself with a simple paste made of baking soda and water. Since this substance is not toxic it should work well for your pet. You only need enough to cover the spot of the sting.