White bread usually molds faster than wheat bread does because the white bread contains more preservatives.
The preservatives are supposed to preserve the bread and make it last longer but actually it makes most breads including the white bread mold faster.
Homemade bread without the preservatives also molds just as fast if not kept in a cool dark place.
The wheat bread contains less preservatives so it molds less fast than white bread.
Another thing is that bread does go bad faster in the heat than it does in the cool no matter what type of bread.
When you have bread in storage you need to make sure that it doesn't get too hot such as staying in too hot of a room.
The heat can cause the bread to dry out and go stale and even mold more quickly.
So make sure to store the bread in a cool dark place if possible.
Or if your kitchen or house has air conditioning the bread should be just fine in the cool house.
Don't leave the bread out in the car in the heat too long either and be sure to bring any bread inside the house and keep it cool as soon as you can.
Bread can be refrigerated if you need too but when the bread is put in the refrigerator it does go bad sooner as well.
It's best to buy just the amount of bread you can reasonably eat within a few days to a week and then get more fresh bread.