All of the currently commercially available hybrids are not plugged in at all; the electricity is generated when you use the breaks. It would have absolutely no effect on your energy bill at all.
Assuming you are talking about a Plug-In-Hybrid here is a reference point for you. My 1988 Mitsubishi MightyMax Pickup used to cost me $140/mo for the 500 or so miles I drive in that time. After I converted it to full electric, my electricity bill only went up $30/mo for the same amount of driving.
Only by 30 cents a day or so..
There are no plug-in hybrids available right now. All hybrids recharge the batteries while driving via various methods like regenerative braking.
Eventually there will be plug-in hybrids (such as the Chevy Volt and plug-in version of the Prius), but they won’t increase your electric bill too drastically. Electric cars and plug-in hybrids cost about 2 cents per mile to recharge. Cars that run purely on gasoline cost on the order of 10 cents per mile to refuel (for gas at $3/gallon).
In other words, your electric bill will go up (by about $20/month if you drive 1000 miles per month), but your total fueling bill will be cut by 80%.