We provide a physical insight into the mechanism of the bulk viscosity zeta and construct a new formula for zeta directly from microscopic information such as the interatomic potential and the pair distribution function. This is an outstanding advantage when compared to the previously proposed formulas in all of which zeta is expressed only in terms of a macroscopic quantity, i.e., pressure. In other words, our new formula makes it possible for the first time to discuss the relation between the macroscopic quantity zeta and the microscopic properties such as the interatomic potential and the pair distribution function. This new formula is derived by solving the time development equation of the pair distribution function. Among some of the previously proposed formulas, we prove that the Green-Kubo formula and the Heyes formula are both equivalent to our new formula when the macroscopic quantity-pressure-in their expressions is described by means of interatomic potentials and pair distribution functions under appropriate conditions. This fact confirms the validity of our formula, which reinforces the aforementioned advantage. We calculate zeta near the triple point of the Lennard-Jones fluid using our formula, the Green-Kubo formula, and the Heyes formula. The obtained values of zeta are in good agreement with each other.