In case any public highway of any county in the state shall cross any river or stream on such highway within the boundaries of any municipality, in whole or in part, and it shall be deemed by the board of supervisors to be to the interest of the public that a free or toll bridge be constructed across such stream at the expense and under jurisdiction of the county, and the municipal authorities of such municipality shall by ordinance express a willingness that such bridge be constructed and maintained at the expense of the county, the board of supervisors are hereby authorized and empowered to establish, construct, and maintain such bridge either as a free or toll bridge, as in case of other bridges of the county and to the full extent as now authorized by law in such cases.