We develop a transfer matrix method to compute exactly the spin-spin correlation functions
〈s0sn〉 of Bethe lattice spin models in the external magnetic field
h and for any temperature
T. We first compute
〈s0sn〉 for the most general spin-
S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin-
S Ising model includes the spin-
21 simple Ising model and the Blume-Emery-Griffiths (BEG) model as special cases. From the spin-spin correlation functions, we obtain functions of correlation length $\ensuremath{\xi}(T,h)$ for the simple Ising model and BEG model, which show interesting scaling and divergent behavior as $\stackrel{\ensuremath{\rightarrow}}{h}0$ and
T approaches the critical temperature
Tc. Our method to compute exact spin-spin correlation functions may be applied to other Ising-type models on Bethe and Bethe-like lattices.