A numerical quantum transfer-matrix approach, to S = 1 macroscopic chains with single-site anisotropy and alternating bonds is worked out in the framework of statistical mechanics, using a real-space decomposition scheme and the Trotter formula for the noncommuting operators. A fit of the experimental susceptibility data for a number of the-uniform and bond-alternating quasi-one-dimensional molecular magnets is performed down to the low-temperature region. New microscopic parameters for the nonuniform systems are established, the characteristic temperature locating the maximum of the zero-held uniform susceptibility is estimated and the temperature behavior of the zero-field susceptibility for different ferro-antiferro coupling ratios is presented.