In most cases, there will be mild swelling and tenderness where the dog was stung, usually on the face or paws.
To stop the venom from spreading, try to remove the stinger as quickly as possible. Removal of the stinger should be done using a credit card to scrape it out.
“If your dog gets stung by a bee and starts vomiting within five to 10 minutes and his gums become pale, that’s when you know they are going into anaphylactic shock.
Full article VetStreet: Bee Stings 101: How to Help Your Pet