ChatterBank20 mins ago
Spelling Bee
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For more on marking an answer as the "Best Answer", please visit our FAQ.The earliest evidence of the phrase "spelling bee" in print dates back to 1825, although the contests had apparently been held before that year..
The etymology of the word "bee" is unclear. Historically, it has described a social congregation where a specific action is being carried out, like a husking bee, or an apple bee
source www.wikipedia.com
The link on Jack's answer above did not seem to work for me, so...
A 'bee', in this sense - most probably so-called after the social, hard-working nature of the insect itself - was a gathering of people, generally neighbours in the USA, to carry out some common task. Thus, you could have quilting-bees, apple-bees (to bring in the fruit from each other's orchards) and so on. A spelling-bee is just such a gathering to compete over who can spell best.