Mine's in factory boxes inside a military surplus ammo can. If I'm going to a competition match, they'll be in the plastic reloading boxes in my range bag.
Regarding the fire hazard, ammo not in a gun is little more than popcorn. Without the barrel chamber to hold the cartridge together, it just bursts apart and the flying brass (bullet mostly stays put because it's much heavier) doesn't even have enough ommph to go through clothing. Worst danger might be getting some shrapnel in your eye and any fireman should be wearing goggles already.