Use them every time you clean. And replace them often. Any time someone calls with any type of fouling issue they are not brushing or they are using a nylon brush. Save yourself grief, brush often. It wont hurt anything.
Honestly, I must comment here. As a matter of site policy we have always encouraged people to clean barrels conservatively. I have nothing against bronze brushes, provided a good fitting bore guide is used and effort is made to not drag grit back across the crown. I personally advise against reversing a brush at the muzzle. I have seen barrels that had accuracy decline and recrowning solved the problem. On close inspection with magnification the crown edge (before recrowning) looked like sharks teeth.
Different cleaning methods are appropriate for different barrels, different cartridges, different powders, different strings of fire. I have some barrels that benefit from bronze brushing, and others that do best with wet patches followed by WipeOut (double application) every 60 rounds or so and virtually no brushing. My best shooting barrel, one which set a club 600-yard record, has never seen a brush.
In the course of running this website for 14 years, I have interviewed multiple record holders, national champs, and world champions. What I have seen is that these guys brush LESS than you might believe, and the definite trend is to use bronze brushes less often and more conservatively. (100/200 Group benchrest shooting is an exception to this -- but many of those guys toss their barrels before 1000 rounds).
For this reason I have replied to Alex's post. I respect Alex, and I do acknowledge that bronze brushes are effective for removing fouling and can be used without damaging barrels. That said I see aggressive bronze brushing as a last resort when other more conservative methods don't work, or as a supplement to other methods, such as wet patching followed by Wipeout.
One thing Alex and I do agree on is the need to regularly remove carbon from the inside of your barrel before the carbon gets thick and hardens. Hard carbon can affect accuracy and you don't want your bore to get to that state. So don't shoot 200 rounds and put the gun away for weeks. I generally clean after 60-70 rounds, when that is possible given the course of fire. My barrels get two applications of foam when they are still warm from shooting, and that obviates much of the need to bronze-brush. Every barrel is different though...
I have discussed bronze brushing with leading barrel-makers including John Krieger. John also advocates conservative cleaning methods, and he certainly believes he has seen barrels his company made damaged by over-zealous bronze brushing. John recommends removing the brush after it exits the muzzle, NOT dragging it back.
I urge all our forum members to find out what methods work best for their barrels, their cartridge types, their powder type, and their shooting style -- learn this by starting conservatively. And by all means, if you have a great barrel that shoots in the ones don't do ANYthing that is likely to change internal dimensions.
Another noted barrel-maker, who asked to remain nameless, told me -- "I have seen plenty of barrels sent to the grave before their time by over-aggressive cleaning. But that is good for my business... so I'm happy to see people saw brushes back and forth and use JB all the time."
To conclude, I do not mean to challenge the many successful shooters who prefer to brush with bronze brushes. If it works for them, that's great. However, I can tell you that the majority of champions (other than 100/200 benchresters) I have talked to over the last decade are brushing less frequently and using bronze brushes more conservatively.