Quantifying the interactions in dense colloidal fluids requires a properly designed order parameter. We present a modified bond-orientational order parameter, ψ̄6, to avoid problems of the original definition of bond-orientational order parameter. The original bond-orientational order parameter can change discontinuously in time but our modified order parameter is free from the discontinuity and, thus, it is a suitable measure to quantify the dynamics of the bond-orientational ordering of the local surroundings. Here we analyze ψ̄6 in a dense driven monodisperse quasi-two-dimensional colloidal fluids where a single particle is optically trapped at the center. The perturbation by the trapped and driven particle alters the structure and dynamics of the neighboring particles. This perturbation disturbs the flow and causes spatial and temporal distortion of the bond-orientational configuration surrounding each particle. We investigate spatio-temporal behavior of ψ̄6 by a Wavelet transform that provides a time-frequency representation of the time series of ψ̄6. It is found that particles that have high power in frequencies corresponding to the inverse of the timescale of perturbation undergo distortions of their packing configurations that result in cage breaking and formation dynamics. To gain insight into the dynamic structure of cage breaking and formation of bond-orientational ordering, we compare the cage breaking and formation dynamics with the underlying dynamical structure identified by Lagrangian Coherent Structures (LCSs) estimated from the finite-time Lyapunov exponent (FTLE) field. The LCSs are moving separatrices that effectively divide the flow into distinct regions with different dynamical behavior. It is shown that the spatial distribution of the FTLE field and the power of particles in the wavelet transform have positive correlation, implying that LCSs provide a dynamic structure that dominates the dynamics of cage breaking and formation of the colloidal fluids.