As stated, brushes are made of bronze, not brass.
Bore Snakes contain an internall woven bronze brush.
The only negative concerning bronze brushes is when they are used in conjunction with modern solvents that remove copper fouling.
Since copper is a component of bronze, the solvents will eat the brush in fairly short order so if you use these products I would strongly recommend sticking with nylon brushes which the solvents will not affect.
I insert the all brushes from chamber or muzzle depending on which is practical and push it through the bore, then I unscrew the brush from the rod, remove the rod from the bore, reinstall the brush and repeat as many times as necessary to loosen the fouling.
This also allows you to clean the brush each time, removing any jacket material or lead chips from the brush.
Running any brush back and forth in a barrel bore only wears the brush out faster from the brush tines being rocked back and forth on the securing wire, it certainly doesn't make the bore any cleaner and by dragging potential pieces of jacket material or what not back and forth in the bore one really does run the risk of scratching the barrel steel in the bore. HTH