After an hour of research:
It seems like the base rate of anaphylaxis from bee stings is about 3%. Anaphylaxis, if it occurs, usually starts within minutes of the exposure to the allergen. (It can occur as much as 24 hours later, but this is "rare". I don't know how rare, quantitatively.)
Anaphylaxis is the result of a "global" or "systematic" reaction, as opposed to a "local" reaction, namely swelling around the area stung.
There is some risk that a local reaction can cause swelling of the throat blocking the airways, but since 43% of bee stings are on the face and neck, and severe respiratory distress is rare, this is is very uncommon. It seems like this is only a concern when the person is stung inside the mouth or throat.
The simple answer is observation.
As long as there's no difficulty swallowing or breathing then the reaction is local only. People with true anaphylaxis experience facial/tongue/mouth swelling and respiratory symptoms regardless of where the sting is.
Any respiratory or oral symptoms should prompt an immediate trip to the hospital.
Facts:
Questions:
[Update: it seems like the base-rate of anaphylaxis from bee stings is 3%, when anaphylaxis occurs, it usually starts within within a few minutes.
The key question I have left is if "large local swelling", can block the air ways when it the swelling is on the head or face.]
Thank you!
Eli