"state of being actively employed," 1849, first attested in Thoreau, from busy (adj.) + -ness. A modern formation made necessary after business evolved away from busy. Middle English had busyship, busyhede.
they manifested all the busyness of a pack of beavers
bustle
bustling
busty
busy
busybody
busyness
busy-work
but
butane
butch
butcher