All airlines will have both a Contract of Carriage and very detailed printed rules for firearms and ammunition on their web sites. Most read that ammo must be in the original box or a sturdy container designed to carry ammunition. It's a little early in the season for these "Flying with Firearms" discussions but it is often recommended to print the posted rules out in case there is a difference of opinion. Last I saw was that some have had problems when they take possession of the firearm in jurisdictions where they would not be allowed to possess any gun. If your flight gets diverted to a very "blue" city be careful before claiming it.
Add - just read SW Air's firearms and ammo section again as a refresher. Number #1 is that the customer is responsible for knowing the laws of the jurisdictions involved.
The containers permissible for the ammo are pretty clear. Before it comes up, it always does, the properly packed ammo can be in the same case as the gun.
