Any bridge lying in any highway or highways which have been constructed by or upon which work has been done by the state under the supervision of the director of transportation, which shall not be constructed, repaired, or reconstructed by the director of transportation before the making of the director’s next annual report, may be included in the director’s next or any subsequent annual report and recommended for construction, reparation, or reconstruction, and the general assembly may appropriate money for the construction, reparation, or reconstruction. And whenever hereafter the director of transportation shall recommend the relocating, regrading, or improving of any highway which shall include any bridge, the bridge shall come under the supervision of the director of transportation, and the legislature shall, upon appropriating money for the relocating, regrading, or improving of the highway, also make a specific appropriation for the construction, reparation, or reconstruction of the bridge according to the recommendations of the director of transportation, except that each public utility using any of the bridges shall repay to the state the portion of the cost of construction, reparation, or reconstruction of the bridges to be determined in such manner as is provided by § 24-8-23. The bridges when so constructed, repaired, or reconstructed shall thereupon become a part of the state highway system, and shall henceforth be maintained by the state, except those bridges which are used by any public utility which shall pay a part of the cost of maintenance of the bridges in the manner provided by § 24-8-23.