Optical emission spectroscopy and fast, time-resolved imaging are used to assess the plasma parameters in the plasma channel of a pulsed power electrical discharge in gas bubbles. Gas bubbles are produced at the tip of a needle electrode submerged in water. The discharge in Ar, O2, and air bubbles is generated by applying 1μs long, 8 - 20 kV rectangular voltage pulses to the needle electrode. Spectroscopic methods based on line intensity ratio measurements and Boltzmann plots of line intensities of Ar, H, Ar +, and the examination of molecular emission bands from N2 molecules and OH radicals provide evidence of both fast, beam-like electrons and slow, thermalized electrons with temperatures of 0.6 - 0.8 eV. The spectroscopic study of rotational-vibrational bands of OH and N2 gives vibrational and rotational temperatures of about 0.9 eV and 0.1 eV, respectively. This investigation provides important experimental information about the characteristics of the plasma in the discharge channel. Accurate experimental information is important for practical applications of discharges in gas bubbles at atmospheric pressure as well as for the theoretical understanding and modeling that cannot proceed without a thorough experimental base.