Even without sugar, bread contains a lot of carbohydrates that break down right into sugar just by coming into contact with the spit in your mouth.
If you think that's not true, simply take a sugar-low bread (check the food label, don't just go for organic/whole-grain, those usually have more sugar) and taste it for a while in your mouth. You'll notice it starts to become sweeter in your mouth.
And that's actually not an issue. As you probably know, glucose is the fuel our bodies and brains run on, and while your body can break down proteins to glucose in a pinch, it's not actually healthy (despite what proponents of ketosis diets will tell you). It's especially hard on the kidneys.
As long as you stick to proper bread without the crazy added sugar, and preferably whole grain (actual whole grain, not just marketing "whole grain"), it's not an issue. Unless you try to subsist on literally only bread, of course.
I'm not talking about various proteins and rather about starch, which is a natural part of a good bread. The enzymes in your mouth and digestive system will break down starch to normal Glucose without a problem.
If you think that's not true, simply take a sugar-low bread (check the food label, don't just go for organic/whole-grain, those usually have more sugar) and taste it for a while in your mouth. You'll notice it starts to become sweeter in your mouth.