Magntetoelectric (ME) multiferroics, which exhibit coexisting magnetism and ferroelectricity with cross coupling, are being extensively investigated because of the scientific importance of the electronic origin of magnetoelectrics and relevant prospective applications in devices, such as the magnetic-field controlled electro-optic or piezoelectric devices, with new functionalities. The multiferroicity is observed in such manganites as RMnO3 (R = Dy, Tb, Gd) and TbMn2O5. In order to design the devices for the potential applications of RMnO3 manganites, it is essential to prepare the thin films with a well-defined crystalline structure. In this study, we report the fabrication of the single crystalline orthorhombic DyMnO3 thin films on different substrates. We investigated the substrate-dependent electronic structure and anisotropic bonding of the Mn 3d states in DyMnO3 thin films on SrTiO3(001) and LaAlO3(110) substrates using polarization-dependent x-ray absorption spectroscopy (XAS) at O K-, Mn L- and Mn K-edges for three polarizations, E || a, E || b and E || c. Polarization-dependent x-ray absorption spectra at O K-, Mn L23- and Mn K-edges of orthorhombic DyMnO3/LaAlO3(110) thin films show strong polarization dependence for three polarizations, E || a, E || b and E || c, whereas orthorhombic DyMnO3/SrTiO3(001) thin films show nearly isotropic spectral structure. The main peak in polarized Mn L2,3-edge XAS spectra of DyMnO3/LaAlO3(110) thin films for the E || b polarization lies at a lower energy than for polarizations E || a and E || c. The disparate spectra for polarizations E || a and E || b indicate a great anisotropy in Mn 3d-O 2p hybridization and charge transfer from O 2p to Mn 3d, reflecting an orbital ordering and a highly anisotropic coplanar Mn-O bonding in DyMnO3/LaAlO3(110) thin films. These results indicate orbital ordering of eg-orbital and thus the highly anisotropic in-plane Mn-O bonding which is an indispensable factor to the formation of complicated incommensurate modulated magnetic structures observed in orthorhombic DyMnO3. Utilizing the technique of epitaxial strain stabilization, one can control electronic structure via growing RMnO3 thin films of the same compound on different substrates. The present results provide important implications for the microscopic understanding of the RMnO3 manganites.