The Talmud discusses the prohibition of trapping an animal, one of the 39 melachot of Shabbat. If the purpose of trapping was not to use the animal (i.e. it’s meat or hide) the prohibition is not Biblical in nature, but only Rabbinic because it is a “melacha she’ayna tzricha l’gufo” – an act that is not intrinsically needed.
As a result, the Talmud [Shabbat 106b] teaches that is someone traps a flea on Shabbat, it is only prohibited Rabbinically. However, Tosafot adds that if the flea was biting the person, it is permitted to trap it, because of the pain it would cause. At the same time, the Talmud rules that a non-poisonous snake is allowed to be captured to avoid its bite. Explained the Beur Halacha [Orech Chaim 316] that the difference in law between a snake and a flea is the amount of pain that it inflicts. Since a snake’s bite inflicts a great deal of pain, it can be captured, while a flea’s bite causes minimal pain and therefore, only when it is actually on a person’s skin (or clothing according to Mishna Berura) can it be captured.
What is the status of a bee? Is its sting more like the bite of a snake, or the bite of a flea?
On this there is a debate. However, there are authorities who rule that it a bee sting is much more painful and therefore, a bee can be captured [The 39 Melachos, R’ Ribiat pp. 872-874]. This is especially true if young children are in the sukkah or if a person is allergic to bee stings.
Interestingly, there is a position that maintains that on Yom Tov, since slaughtering of animals is permitted, bees should be killed (“mi’toch sh’hutra l’tzorech hutra nami sh’lo l’tzorech”), while on Shabbat bees should be trapped [Minchat Shlomo 2, 60:28, b’Mareh Bazak 7:54].
