Do high wattage power supplies cost more to run?

No - the rated wattage of a power supply refers to the maximum amount of power it can deliver at full load, not how much power it uses. More powerful PSUs will consume around the same amount of power as lower powered power supplies in any given PC system, so your electricity bill will not be higher when using a more powerful power supply!

The best way to reduce your electricity bill when using your PC is to use a more efficient power supply or make your PC consume less power by removing components which are not needed, such as extra drives and expansion cards, or by choosing a cooler-running processor or graphics card.