Dependence of the phase and magnitude of the response of MgO substrate YBa2Cu3O7-δ (YBCO) transition edge bolometers to the near infrared radiation on the superconducting transition width is presented in this work. The bolometers were made of YBCO thin films of 200 nm thickness that were grown on single crystal MgO (1 0 0) substrates by DC inverted cylindrical magnetron sputtering. We have measured the responses of both large and small area devices with respect to the bias temperature and radiation modulation frequency. We have observed that the superconducting transition width has major effects on the response of the bolometers such as; on a dip of the phase of the response versus modulation frequency curve around 1 Hz, the rate of decrease of the magnitude of the response, and dependence of the phase of the response on temperature at mid-range modulation frequency. We have investigated a correlation between the superconducting transition width and the YBCO film surface morphology of the devices. In addition, the illumination wavelength dependence of the optical response of both wide and narrow transition width devices has been investigated. Here we present the analysis and the possible mechanisms that can affect the response of the bolometers at the superconducting transition region.