A very common word in English, business is not uncommonly mis-spelled. I suspect that this is because it is pronounced with only two syllables (biz_nis, SAMPA: /"bIzn@s/) - although it looks as though it has three.
It may help those with problems to notice that it is derived from 'busy' + '_ness', and the '_y_' has become an '_i_'. It probably won't, however: such writers will just have to memorise the correct spelling: b + USI + ness.
If you want to use a three syllabled word meaning 'the state of being busy', spell it busyness.
Do not spell it
busyness if you are talking about business studies or the sort of thing that business students study.