The dependences of the static dipole polarizabilities per atom (PPAs) on the bonding and shape of selected stoichiometric aluminum phosphide clusters (ground states and higher lying species) of small and medium sizes have been comprehensively studied at Hartree-Fock and the second order Moller-Plesset perturbation levels of theory. It is shown that the nonmonotonic size variations in the mean PPAs of AlP species which maintain closed cagelike structures, frequently observed in clusters, are directly related to covalent homoatomic bonds inside each cluster's framework. Accordingly, the PPAs of clusters which are characterized by one or more bonds between the Al and P atoms are larger than the PPAs of clusters with the uniform alternating Al-P bond matrix. This is caused by the electron transfer increase from the electropositive Al to the electronegative P atom with the cluster growth. This transfer is larger for the clusters characterized by alternating Al-P bonding. The later effect explains the decrease in the PPA of AlP species which maintain closed cage-like structures, with the cluster growth. However, this picture drastically changes for artificial metastable prolate species built up by the ground states of smaller clusters. It is demonstrated that for prolate binary AlP clusters of medium size, the shape dominates against any other structural or bonding factor, forcing the PPA to increase with the cluster size. Nonetheless, as the cluster size grows, it is predicted that the PPAs of the studied prolate clusters will saturate eventually with the cluster size. Also, it is verified that the theoretical predicted polarizabilities of AlP semiconductor clusters are larger than the bulk polarizability in accord with other theoretical predictions for similar systems. Lastly, it is pointed out that major bonding or structural changes should take place in order the convergence with the bulk polarizability to be accomplished since it is revealed that the size increase is a necessary but not a sufficient factor for the cluster to bulk transition.