The transport properties, including electrical resistivity ($\ensuremath{\rho})$, thermopower $(S)$, and thermal conductivity $(\ensuremath{\kappa})$ of bulk metallic glass alloys ${\mathrm{Cu}}_{64}{\mathrm{Zr}}_{28.5}{\mathrm{Ti}}_{7.1}$, ${\mathrm{Cu}}_{62.3}{\mathrm{Zr}}_{23.7}{\mathrm{Ti}}_{10}$, ${\mathrm{Cu}}_{60.6}{\mathrm{Zr}}_{26.9}{\mathrm{Ti}}_{12.5}$ and ${\mathrm{Cu}}_{58.8}{\mathrm{Zr}}_{26.2}{\mathrm{Ti}}_{15}$ in the temperature range $10--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are reported. The temperature variations of electrical resistivity in these alloys, with a negative temperature coefficient, are found to be rather weak. These findings are consistent with the metallic glass nature of these compounds. It is observed that the electrical resistivity increases with increasing Ti concentration, ascribed to the enhancement of disorder with such a composition change. The magnetoresistivity of ${\mathrm{Cu}}_{64}{\mathrm{Zr}}_{28.5}{\mathrm{Ti}}_{7.5}$ alloy decreases with increasing temperature and increases with increasing magnetic field, suggesting that the weak localization effect dominates the electrical transport. The temperature-dependent thermopower and thermal conductivity characteristics are nearly identical and weakly independent of compositions. It is noted that the observed $\ensuremath{\kappa}(T)$ of Cu-Zr-Ti metallic glass alloys show notable similarities with the quasicrystalline system. There are two main features in $S(T)$, a knee around $120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and a plateau below $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which represent the deviation from the expected linear behavior. A detailed theoretical analysis has suggested that the appearance of the knee is due to the electron-phonon interaction at low temperatures and the plateau is associated with low-energy excitations in glasses.