Eight. The board’s perimeter consists of 14 black and 14 white squares, and one bishop can’t control more than 4 squares on the border. That means we’ll need at least 4 white bishops to cover the 14 white border squares, because 3 bishops could cover at most 12. Similarly we’ll need at least 4 black bishops to cover the 14 black border squares. As it happens, a row of eight bishops across either of the board’s two middle ranks does the job, so the minimum needed is 8.