There are several variables that affect the answer to this question. How old is the house, and how old its accompanying HVAC? How big is the house? How many people are in the household? Does the home have a pool? Is it Summer or Winter? Do you insist on it being below 72 degrees day and night in the Summer? Do you insist on it being above 80 degrees day and night in the Winter? How many SEER is the A/C? How many windows are in the home, and which way do they face? And even down to the questions of do you have the window coverings open or closed? Does the home have "Low E" windows?
SEER stands for Seasonal Energy Efficiency Rating. The higher the SEER, the more efficient the A/C. If the SEER rating is 13 or above, you have a very efficient air conditioner. If it is under 12, no so much. regardless of the number of bedrooms, the bigger the house, the more energy it is going to take to heat and air condition.
"Low E" refers to "Low Emissive" windows that were constructed such that they had an inert gas, typically argon in between the panes of glass. The result was there was less transmission of heat into the home or cool out of the home (in summer - reverse that for winter) through the windows. By the way, the windows are the most vulnerable part of a home when it comes to ingress of heat or egress of cool, either through radiation or conduction. A home with "Low E" windows is obviously more energy efficient and will use less electricity to cool, or gas to heat. "Low E" windows are not cheap, so it was not a given that they put them in. Prior to 1994 or so, you never see "Low E" windows in use. Do to competitive pressure, I suspect that now almost all new homes have "Low E" windows.
Incidentally, with rare exception, and then only in homes built prior to 1988, most homes here use electricity for cooling and gas for everything heat related - cooking, heating the home in Winter, and water heater.
But, to the heart of your question, I have seen electric bills as low as $125 to as high as $300 in the Summer. Monthly Gas bills generally run in the $50 to $150 range, unless you have a pool. If there is a pool, add $150 (plus or minus $50) per month to the utilities (total cost of maintenance) year round. Every few years for the decade between 1995 and 2005, the MECs (model energy code) were revised, increasing the energy efficiency requirement, so homes just keep getting more energy efficient the newer they are.
In an effort to differentiate themselves from the competition, some Builders entered into an agreement with EnergyStar, subject to passing an engineering review of their homes proving that they had attained a certain high level of efficiency so they could place the EnergyStar brand on their homes and use the Logo in their advertising. Those who didn't obviously had higher utility bills than those who earned the EnergyStar rating.
I hope this helps.
best of luck, and thanks for reading.
Do you shower once or twice a day? Do you have computers and TV's running all the time? Do you let your air / heat run heavily all day? How many people are occupying the home?
Home: How large is the home? How far do the utilities need to travel? How much space do you need to cool / heat? How many occupants? How many TV's, Computers, etc.?
Unfortunately, there is not direct answer to this very generalized question.