We investigated the electro-optic response in the "foggy" amorphous blue phase (BPIII) as well as in the isotropic phase. To the best of our knowledge, such a study has not yet been performed due to the very limited thermal range of BPIII. In this study, we used a single-component chiral bent-core liquid crystal with a self-stabilized BPIII, which is stable over a wide temperature range. The results show that the response time is on the order of hundreds of microseconds in the isotropic phase and increases to 1-2 ms in the BPIII (at TI-BP-T < 1), then drastically increases up to a few tens of milliseconds upon further cooling in BPIII. Such an unusual behavior was explained on the basis of the high rotational viscosity and/or the existence of nanoscale smectic (Sm) clusters. The Kerr constant was also measured and found to be similar to 500 pmV(-2), which is the largest among bent-core BP systems reported so far and comparable with that of polymer-stabilized BPs.