This is the 3602nd most frequent Japanese word.
運ば
"運ば" means "carried" or "transported."
運ば is used in its base verb form here, 運ぶ, meaning 'to carry or transport.' It indicates the action of moving luggage.
重い荷物を運ばなければならない。
I have to carry heavy luggage.
運ば in this sentence is part of the passive form 運ばれる, meaning 'to be transported or carried.' It describes the movement of the ball caused by the wind.
風に吹かれ、ボールが庭の隅まで運ばれた。
Blown by the wind, the ball was carried to the corner of the garden.
運ば here is used metaphorically in the passive form to imply steering or leading a conversation towards a specific direction.