I have been using a bag just like this one below for 6 years. I travel for a living and it comes with me on about 20 round trip flights x 6 years and it looks like its in great shape still. very easy to go from the rental car to the course. only difference is mine has wheels on the bottom that i dont see in this pic.
it fits all my clubs, dozen balls, hats, towels, tees etc... fully setup, ready to play
I can only speak for united airlines, they consider it another bag. if you have the points, they dont charge you otherwise its $35 to check a bag i believe
http://www.ebags.com/product/caddy-daddy-golf/co-pilot-xl-hybrid-travel-bag/242722?productid=10212825&sourceid;=ADWPRODUCT&couponid;=55583734&gclid;=CLm48Pm0_rkCFdSY4AodVS0AvQ&kwid;=productads-plaid^56402570058-sku^10212825-adType^PLA-device^c-adid^26970782778