The closest "major" airport to Antelope Wells is El Paso, TX. The next is Tuscon, AZ. There are bike shops in both cities that can pack and ship your bike. You could also take Amtrak in either city. Amtrak sells a box that fits just about anything other than a tandem or recumbent. Personally I prefer to take Amtrak. It may take longer but the lack of hassle is worth it. You could also use one of the bike shipping services after a LBS packs it for you.