Unless you are planning on engaging in a conflict somewhere......
A couple boxes of cartridges is all you need, in fact, I take a half box for each rifle and I usually take 2 rifles so thats one box of 20 or 10 per. That allows me a couple fouling shots prior and 5 for the hunt. If you need more than 5 for the hunt, you better go practice somewhere..............
I put mine in my luggage. TSA regs say the ammo must be seperate from the firearm.
Don't forget to have the magazines removed and the rifles stowed in a TSA approved case (gorilla proof), with TSA approved (cheapo) locks attached and have the rifles in the case with the serial numbers showing.
I don't remove the bolts and never had an issue, though some remove the bolts.
Don't chintz on a case. Forget the cheap Plano crap. Thats fine for the range but it won't last one trip on an airplane because the baggage jockeys will use your rifle case for volleyball practice.....
I'm sold on Pelican Storm Cases or a top end Cabelas aluminum, reinforced gun case with locking bar.
Things get lost (guns included) so I take one exotic tifle and one plain jane. That way, if my ammo gets lost with my luggage (happens), I can get plain jane ammo at the local wallyworld.
Better safe than sorry.....
Have fun.