(a) The county governing authority may contract and pay out of the funds of the county such sums of money as it deems equitable and just to the authorities of the United States for the county's fair proportion of the cost of building any bridge which it deems necessary to erect across any stream dividing the county or some part thereof from lands over which the jurisdiction has been ceded to the government of the United States for any purpose, provided that it shall thereafter be the duty of the authorities of the United States to keep such bridges in repair, to renew them as often as may be necessary, and to keep them open for the free and uninterrupted travel of the public.

(b) The United States is vested with full and complete jurisdiction over grounds necessary for the erection of piers and approaches to such bridges on each side of such streams, so far as may be necessary for the erection, repair, and protection of the bridges and approaches.