The method of providing for the payment of the cost of constructing the bridge or tunnel and the expense of operating and maintaining the same, so far as such cost and expense shall be a charge upon the counties consenting to the appointment of the commission, shall be determined by the governing bodies of such counties in agreement with the commission. Such cost and expense shall, by the terms of the agreement, be distributed among said counties and borne by each of them in such proportion as may be set out in the agreement. From time to time as the building of the bridge or tunnel progresses, the commission may require each of the counties to pay the commission its proportionate share of the cost of building and maintenance.