Well, to be honestly speaking, mainay kabhi gaur nai kia regarding savings in electricity bills! 
Regarding cooling of DC Inverter vs Non-Inverter AC, yes, it may be true that cooling of Non-Inverters is abrupt and fast as compared to their DC Inverter counterparts, but aisi baat nai hai k Inverters cooling hi nai kartay ya kamm kartay hain. Both have different working schematics.
As per my limited knowledge, Non-Inverter ACs' compressors work on 0/1 logic, either they are working at full capacity or are not working when desired temperature is achieved; they trip.
Well, this is not the case with DC Inverters, their compressors' motors' rpm keep on fluctuating and are never constant / fixed. When you start your DC Inverter, it draws less current as compared to Non-Inverter AC. Accordingly, rpms are low and cooling may be slow, but then, rpms increase, wattage increases and cooling is attained, but it takes more time for DC Inverter to cool than a Non-inverter.
I don't know, but some people even say that cost to benefit ratio of DC Inverter vs Non-Inverter is the same.
And Yes, in areas where there is extreme load shedding, DC Inverter is not recommended.