Very recently, as an important step in the development of layered Fe-free pnictide-oxide superconductors, the new phase BaTi2Bi2O was discovered which has the highest TC (about 4.6 K) among all related non-doped systems. In this Letter, we report for the first time the electronic bands, Fermi surface topology, total and partial densities of electronic states for BaTi2Bi2O obtained by means of the first-principles FLAPW-GGA calculations. The inter-atomic bonding picture is described as a high-anisotropic mixture of metallic, covalent, and ionic contributions. Besides, the structural and electronic factors, which can be responsible for the increased transition temperature for BaTi2Bi2O (as compared with related pnictide-oxides BaTi2As2O and BaTi2Sb2O), are discussed.