The three lowest-lying electronic states, (X) over tilde E-1(+), (a) over tilde (3)Pi and (A) over tilde (1)Pi, of the linear BBO molecule have been systematically investigated using ab initio electronic structure theory. The equilibrium structures and physical properties including dipole moments, vibrational frequencies and associated infrared intensities, Renner parameters and energetics for the three states of BBO have been determined employing SCF, CISD, CCSD and CCSD(T) levels of theory and a wide range of basis sets. The ground state of BBO presents a degenerate real bending frequency, while the (a) over tilde (3)Pi and (A) over tilde (1)Pi states show two distinct real bending frequencies due to the Renner-Teller interaction. The bending motion of the (A) over tilde (1)Pi state was analysed using the equation-of-motion (EOM)-CCSD and EOM-CC3 techniques in order to avoid possible variational collapse to a lower-lying state. The (X) over tilde (1)Sigma(+)-(a) over tilde (3)Pi separation was predicted to be T-0 = 16.6 kcal mol(-1) (5800 cm(-1), 0.719 eV) at the cc-pVQZ CCSD(T) level of theory. With the cc-pVQZ EOM-CC3 method the (X) over tilde (1)Sigma(+)-(A) over tilde (1)Pi splitting was predicted to be T-0 = 48.0 kcal mol(-1)(16800 cm(-1), 2.08 eV), which is in good agreement with the experimental value of T-0 = 46.6 kcal mol(-1) (16 300 cm(-1), 2.02 eV). The Renner parameters and averaged harmonic frequencies of the bending mode were determined to be epsilon = 0.184 and omega(2) = 363 cm(-1) for the (a) over tilde (3)Pi state, and epsilon = 0.246 and omega(2) = 383 cm(-1) for the (A) over tilde (1)Pi state. The theoretical (X) over tilde (1)Sigma(+) state harmonic B-B stretching frequency omega(3) = 636 cm(-1) is somewhat higher than the experimental estimate of 582 cm(-1) and the predicted (A) over tilde (1)Pi state harmonic B-B stretching frequency omega(3) = 861 cm(-1) is significantly higher than the experimental estimate of 440 cm(-1).