I hate to admit this, but I used to work as airport security (that was a while ago, I personally can't stand what they're doing to people now...but that's another story for another day). The airport I worked at was one with a large percentage of hunters and other gun enthusiasts. Basically, even a single round of ammunition means paperwork, and possibly getting a LEO involved. For those that had magazines found in their bag, you're lucky the guy working there didn't classify it as a gun part, or you could have potentially been in for a relatively hefty fine.
The advice I always gave was don't use your hunting/range bag as a travel bag. If you're going to travel with your hunting/range bag, either THOROUGHLY search through it and make sure there's not even a single loose round, or just check it. Loose ammo in a checked bag, though still not allowed (it has to be properly packaged) has the potential for getting you in a lot less trouble, lol.