Yes store bought bread is considered to be a processed food and store bought bread is a processed food.
Food that is processed food goes through a process so that it is preserved and other ingredients are added to it to make it last longer and taste better.
So when you buy store bought bread it is processed.
It's not bad for your health though because even though the store bought bread is a processed food it's not as bad for you as other processed food such as processed meats.
Processed foods also include Pastrami as well as other foods such as beef jerky, corned beef, hot dogs, ham etc.
Any meat or other foods that go through a curing process or a smoking process, is salted or any meat that goes through a process that alters it's taste or to preserve it or enhance the flavor of the food is processed food.