Each member of the board of directors shall give bond in such amount as shall have been fixed by the county board of the county, conditioned to faithfully perform the duties of a director, and of such further office as he may be elected to, and to account for all funds or property coming into his hands. All of such bonds shall run to the district, shall be signed by a surety or sureties to be approved by the county clerk, and shall be filed and recorded in his office. When so filed such person so elected shall take and hold office until his successor is elected and qualified.