Thermocapillary convection driven by surface tension gradient undergoes a series of bifurcation and ultimately evolves into a chaotic state, while temperature difference between the upper and lower ends of the liquid bridge increases. This study employed three-dimensional numerical simulations to investigate the convection transition for Prandtl numbers(Pr) of 0.01 and 0.02 with aspect ratio (a ratio between height to radius) of 1 under microgravity. This study utilized time series spectrum analysis and dynamic mode decomposition to elucidate the spatiotemporal structure of the flow field. The results show that thermocapillary convection in liquid bridges with Pr=0.01 and Pr=0.02 transitions to turbulence through quasi-periodic bifurcation pathways. Specifically, the Pr=0.01 case exhibits a two-frequency quasi-periodic oscillation with frequency-locking characteristics, while the Pr=0.02 case demonstrates a three-frequency quasi-periodic oscillation. During the periodic oscillation stage, thermocapillary convection in liquid bridges with Pr=0.02 shifts from pulse oscillation to rotational oscillation, with wave number changing from a mixture of 1 and 2 to a dominant 2. In contrast, the Pr=0.01 case remains pulsed in both periodic and quasi-periodic phases, with a wave number that remains a mixture of 1 and 2.