Said petitioners shall at the time of filing their petition with the board, file a bond executed by one or more of their number as principals, and in behalf of all, and by a surety corporation authorized to become surety upon public bonds in this state, which bond shall run to the state of Washington as obligee and be in the sum of five hundred dollars, conditioned that they will pay all costs of the proceeding in case for any reason the petition shall not be granted, or in case no fund shall thereafter be created for the payment of the expense attending said proposed waterway improvement. And said petitioners shall, from time to time as the board shall estimate and order, pay the costs and expenses of such proceeding.