How quickly does a bee die after stinging?

Bluntly, in the case of a mass attack by Africanized bees it can be hours to days before the person dies. In the case of an extreme anaphylactic reaction to a bee sting in the worst case it can be less than an hour.

Now let's get this in proportion.

Mass attacks by Africanized bees are very unusual and you need roughly 20 stings for every kilogram of body weight (roughly ten per pound) to reach a potentially fatal level.

As for anaphylaxis, there are about 100,000 cases a year in the US, only one percent of which prove fatal. But this is allcases of anaphylaxis and there are many causes including allergy to nuts, eggs, milk, peanuts, shellfish, wheat, fish, soy, latex, antibiotics, anesthetic drugs, x-ray contrast media, analgesic opioids, non-steroidal anti-inflamatory drugs (aspirin, ibuprofen, and so on), and insect stings (bee, wasp, ant, etc).

Figures world-wide seem to put bee sting mortality at 0.02 per million population. So, the risk of dying from a bee sting is very, very small.