Nothing wrong with a bronze brush, but beware using the ones with a steel core. Here's how I do it:
Get yourself some 1/4" brass tubing from your local hardware store. Using a hacksaw or a Dremel cut-off wheel, cut a slot in one end. Jam an appropriate sized wad of bronze wool in the notch........chuck it up in your hand-drill and commence to getting your chambers spotless. With the right length of tubing, this regimen can also be used to target a lead/carbon fouled part of a pistol barrel(forcing cones come to mind) as well. If you cannot find bronze wool at your local hardware store, try a marine supply store. This is much cheaper than going through a bunch of bronze brushes.................your welcome!