Transient Response is directly proportional to Bandwidth. Bandwidth can be simply defined as the highest frequency till the output=input. Every CMOS system is a low pass filter ie it will allow the low frequencies to go as it is but the higher frequency will be attenuated by a certain amount as dictated by the transfer function of the system. Frequencies get attenuated because the 1/jwC (w is the frequency) tends to reduce the impedance offered.
Transient response is for pulse with a certain rise time which means it has all the frequencies as a factor of 1/Tr(rise_time). So higher the BW more high frequencies will go to output undisturbed.