After a strong electric bias field is applied to the polyester glass Mylar at temperatures in the mK range, its dielectric constant increases and then decays logarithmically in time. We observed its dielectric response for several temperatures and different field sweeps. Starting from the dipole gap theory, we developed a model suggesting that the change in dielectric constant after transient application of a bias field is only partly due to relaxational processes. In particular, nonadiabatic driving of tunneling states (TSs) by applied electric fields causes additional dielectric response. Also, we find that for T less, similar 50 mK the relaxation of TSs is caused primarily by mutual interactions.