A very common word in English, business, is not uncommonly mis-spelled. AWE suspects that this is because it is pronounced with only two syllables (BIZ nis, IPA: /'bɪz nɪ (or ə) 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.
This is one of the 117 mis-spellings listed as 'Common difficulties' in the section on 'Spelling' within 'Writing' in UEfAP.