There are dozens of "brass" and "bronze" alloys.
Get one that has no lead in it. Lead makes the Machinist very happy but the barrel not very strong across the grain.
Ampco has several good & more or less available grades.
The best are miserable to machine Tool wear from the aluminum content contributes, I suppose.
Having said this, bronze is a poor chice for a rifle barrel. Won't dampen vibrations (rings like a bell . . .) so may be less accurate. And for te same size, a bronze barrel is a little over half as stiff as steel. Will "whip" more. Does not rust in the rain but moist powder fouling corrodes it. Keep away from ammonia, horse barns, mice or too much Brasso, can cause those spider cracks with timr. They are real cracks.
Looks real pretty, though. Best kept for pistol barrels in my opinion.
Jim K, RETIRED metalurgist