The motion of bubbles in a two-dimensional bubble column was characterized by the deterministic chaos analysis of time-series data of bubble frequency, measured locally by an optical transmittance probe with a narrowed He-Ne laser beam. To diagnose the dynamics of bubble motion, three different methods were applied to the series of time intervals between two successive bubble passages : (i) the correlation dimensions were estimated from the reconstructed attractors, (ii) using the short-term predictability analysis, the deterministic and random features in the bubble motion were characterized in terms of Mann-Whitney statistic, and (iii) the value of the Hurst exponent was computed using the rescaled range (RIS) analysis. All three parameters were found to show consistent and significant changes at the transition between homogeneous bubble flow and heterogeneous churn-turbulent flow. These results indicate that at low velocity the motion of bubbles in the bubble column is deterministic chaotic whereas at high gas velocity the random-like motion of bubbles becomes significant.