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We investigated the electronic structure and stability of the hexagonal perovskite ${\text{Ba}}_{3}{\text{Ti}}_{2}{\text{RuO}}_{9}$ using high-resolution electron energy loss spectroscopy and first-principles band structure calculations. The comparison between experimental and theoretical results leads to a coherent picture of the electronic structure of this compound where both Ti and Ru ions are tetravalent, the first unoccupied states being of $\text{Ru}\text{ }4d$ character. Structural relaxations performed on four variants of this compound allowed a detailed investigation of the influence of the Ru atoms location in the hexagonal unit cell and clarified the origin of the stabilization of this phase at room temperature. Two structures without inversion symmetry built, respectively, with two ${\text{TiRuO}}_{9}$ units (space group $\text{P}{6}_{3}\text{mc}$, 186) or with one ${\text{Ru}}_{2}{\text{O}}_{9}$ and one ${\text{Ti}}_{2}{\text{O}}_{9}$ unit $(\text{P}\overline{6}\text{m}2,187)$ are found to be the most stable. The stabilization of the first structure occurs through the polarization of the partially filled $\text{Ru}\text{ }4d$ bands, whereas a direct metal-metal bonding interaction taking place between the two Ru atoms in the ${\text{Ru}}_{2}{\text{O}}_{9}$ unit lowers the total energy of the second. The influence of the exchange correlation functional used to perform these calculations on the relative stability of the four variants is discussed.