We report the first measurement of resolved molecular absorption lines with dual-comb spectroscopy using a Kerr-lens mode-locked bidirectional Ti:sapphire ring laser cavity. A 3 nm broad spectrum has been recorded in 5.3 ms with a spectral resolution of ≈ 1 GHz (0.05 cm-1) corresponding to a relative spectral resolution of 2.5 × 10-6. The measurement of spectrally resolved molecular absorption lines have been demonstrated on the oxygen A-band at 394 THz (760 nm, 13 000 cm-1) and was obtained with two free-running 100 fs Ti:sapphire trains of pulses without the need for active phase stabilization protocol nor real-time or post-processing correction. This work demonstrates that the bidirectional laser configuration enables a sufficient level of absolute and mutual coherence for dual-comb spectroscopy of resolved molecular absorption lines. Considering the high versatility of Ti:sapphire emission spectral range (from 600 to 1100 nm) with high-peak powers, the here reported results pave the way for Dual-Comb spectroscopy in the UV range at mW average output power using a standalone set-up, in the aim to extend its applicability for atmospheric remote-sensing.