‘The bee's knees', The snake's hips, the eel's heels, the gnu's shoes and the cat's pyjamas are just a few of the others. The most modern of these phrases in British English refers to the dog's testicles, using an 8-letter word beginning with ‘b' and ending with ‘ocks'!
One theory states ‘the bee's knees' is a mispronounced version of ‘the business' another way of saying ‘the very thing', too. This is extremely dubious and the same applies to the suggestion that ‘the dog's b's' is a corruption of ‘deluxe box', a reference to the best of the Meccano sets. There's no shred of evidence that either is true.
The very earliest recorded uses of ‘the bee's knees' in writing are very close in time. It first emerged in 1922 and the following year it also appeared in H C Witwer's Fighting Blood.
Many of these phrases might have been around in speech beforehand, of course, but they are so close in time that we will probably never know which was the original.
On a human level, there were at least two women with famous knees at the time. The first was the actress, Clara Bow, usually called "The It Girl". She was sometimes nicknamed ‘The Bee' - a reference to the initial letter of her surname. The second was ‘Bee' Jackson, a noted New York dancer.
The plain fact is that we simply do not know how this phrase-craze started, which came first or why.