I find it interesting that they decided to call a spelling competition a spelling bee. How did the word bee come to also mean a competition, not just an insect?
The bee part isn't restricted to competitions; it more generally means a gathering:
A bee, as used in quilting bee, working bee or spelling bee, is an expression used together with another word to describe a gathering of peers to accomplish a task or to hold a competition.
Etymonline offers this history:
[...] Sense of "meeting of neighbors to unite their labor for the benefit of one of their number," 1769, Amer.Eng., is from comparison to the social activity of the insect; this was extended to other senses (e.g. spelling bee, first attested 1809; also hanging bee "a lynching").
Wikipedia's entry contests this:
Because the word describes people working together in a social group, a common false etymology is that the term derives from the insect of the same name and similar social behavior. According to etymological research recorded in dictionaries, the word in fact probably comes from dialectal been or bean (meaning "help given by neighbors"), which came from Middle English bene (meaning "prayer", "boon" and "extra service by a tenant to his lord")
They have Merriam-Webster listed as a source. Thus, the specific origin of bee in this sense is ambiguous. The term spelling bee, however, is just a variation of the usage and appears to have been introduced in the early 1800s.
The term "bee" originally meant:
a community social gathering at which friends and neighbors join together in a single activity (sewing, quilting, barn raising, etc.) usually to help one person or family. The earliest known example in print is a spinning bee, in 1769. Other early occurrences are husking bee (1816), apple bee (1827), and logging bee (1836). Spelling bee is apparently an American term. It first appeared in print in 1875, but it seems certain that the word was used orally for several years before that.
So a "spelling bee" doesn't refer so much to a competition as such, but more to a gathering of people in order to partake in the singular action of spelling.