An Etymological Dictionary of the German Language/Besen
Besen, m., ‘besom, broom,’ from the equiv. MidHG. bësen, bësem, bësme, OHG. bësamo; it corresponds to AS. besma, E. besom, Goth. *bisma, which have the same meaning; a pre-Teut. word of obscure origin; perhaps Beere and Bast are allied. Since the Eng. dialects point to an AS. bîsma, ‘besom,’ it is possible that the word is connected with Bieswind, and the Teut. root bī̆s, ‘to move in a restless, excited way.’
Besen Lat. ferula, 'ferula,' is perhaps connected with this word; base bhes.