The affairs of the district shall be managed by a board of directors chosen from among the electors of the constituent municipalities as follows: Each municipality shall have at least one director. Municipalities with a population, according to the most recent federal census, from twenty-five thousand to one hundred thousand, inclusive, shall have two directors. Municipalities with a population over one hundred thousand shall have four directors. The directors shall be appointed for terms of four years, except that, in municipalities having more than one director, one-half of those first appointed shall serve for two years and one-half for four years, their successors to serve for four years each. Any municipality in respect to which a vacancy on the board occurs shall fill it for the unexpired portion of the term. Section 9-167a shall apply to the appointment of the directors representing each municipality. The directors shall be appointed by the elected chief executive of a city or borough, the board of selectmen in the case of a municipality in which the legislative body is a town meeting or by the board of selectmen of a town with the approval of the legislative body. Notwithstanding the provisions of this section, directors appointed from any municipality which is a member, or becomes a member, of any transit district in existence on May 18, 1972, shall be appointed by the legislative body of each municipality or the board of selectmen in the case of a municipality in which the legislative body is a town meeting. The population of each municipality according to the most recent federal census shall be divided by the number of directors representing such municipality. Each member of the board of directors shall be entitled to cast that number of voting units which is the multiple the population he represents, rounded to the nearest one hundred, is of the smallest population represented by a member, rounded to the nearest one hundred. The directors shall meet at least four times annually or more often on the call of the chairman and shall elect officers from among their number. They may adopt bylaws and rules for the conduct of the affairs of the district. They shall appoint and fix the salary of a district manager, who shall be the chief executive officer of the district, and such other employees as are required for district purposes. Each officer or employee of such district who is the repository or custodian of any funds of such district shall give such bond as is required by the board of directors, with sufficient surety, conditioned on the faithful discharge of his duties. The premium upon such bond shall be paid by the district.