The board of trustees shall elect from its members a secretary and treasurer whose duties it shall be to keep full and correct minutes of all the proceedings of the board of trustees, and keep a separate itemized account of all the expenditures and disbursements by said board of trustees. Said minutes and accounts shall be open to public inspection at any time on demand of any taxpayer in such district. The secretary and treasurer shall give bond in a sum to be fixed by the board of county commissioners for the faithful performance of his or her duties in some reputable bonding company authorized to do business in the state, and said bond shall be made payable to the Governor of Florida and the Governor’s successors in office.