The "real" OED (which requires a subscription to access) has a definition for this spelling:
The state or condition of being busy; busy quality or activity; = business
That's a completely separate entry from the main one:
I. The quality or state of being busy. Obs.
I. 1. Anxiety, solicitude, care; distress, uneasiness. Obs.
I. 2. Diligent labour, exertion, effort. Obs.
I. 3. Application or commitment to a task or purpose; industry, diligence. Obs.
I. 4. Eagerness, earnestness, importunity. Obs.
I. 5. Fuss, ado.
I. 5a. Trouble, difficulty. Obs.
I. 5b. Disturbance, commotion; (also) an instance of this. Obs.
I. 6. Care, attention, observance. Obs.
I. 7. Activity, briskness, motion; = busyness n. Obs.
I. 8. Mischievous or interfering activity; prying, officiousness. Obs.
II. Something with which a person is busy or occupied
(This section also contains many obsolete definitions, but it's where current usages are defined).
I know that's a lot of "cut & paste" (I did have to work on the formatting though! :). I'm probably a typical "reasonably educated" Anglophone, in that before looking it up I didn't really expect to find a "current, valid" entry for the non-standard spelling in OED.
But I'm sure I'll have used it myself many times over the years - though probably more often than not I'd have used "scare quotes" to alert my reader that I'm using a somewhat "facetious" spelling purely in order to positively and unambiguously convey the state of being busy meaning.
TL;DR: The "word" has been around in English for well over 600 years, long before there was anything remotely like a standardised spelling. Ever since printed material became widespread, the i spelling has been "standard" (compare relative prevalence in that NGram link).
But the word had already acquired so many different meanings that by 1809 at least some people were attempting to reclaim the "core" sense of the word by associating it with the y spelling. Probably most people who ever use it today are like me, and think of it as...
quaint spelling, but useful if you want the semantically precise but relatively uncommon meaning.
It's a small sample size, but note that Google Books claims 27 instances of the busyness of the bee, as compared to just three for the business of the bee (none of which show the full context, so they may not even be for the sense under consideration).