You only need to have something to carry your loaded magazines / ammo on your person as you run the course. A simple bag to toss all of it in, your pants pockets, or some sort of carrier designed for the job (vest, chest rig, battle belt, etc. with magazine pouches.)
The thing to think about is this: While you are carrying your stuff, trying to run, do you want it bouncing around in a bag, or possibly falling out of pockets? How will your carrying method hold up under stress? Will it work after getting wet (rain or snow) or muddy? Do you want to risk losing ammo somewhere on the course? I know at least one person lost a few shotgun shells last time (I saw them laying on the driveway), and I heard someone dropped a pistol magazine too?