I've shipped my bike three times via FedEx and it's worked swimmingly.

FedEx Home Delivery is very inexpensive; if you don't have someone's home you can have the bikes sent to, even the regular express service is cheaper than taking it on a plane. Plus you don't have to schlep the box around the airport along with the rest of your luggage - a major plus. If you're staying in hotels, receiving shipments for arriving guests is SOP, just let the front desk know ahead of time.

You should be able to rent a full-sized van pretty inexpensively from a truck rental place, which will give you more passenger space than a box truck, plus being easier to tie your assembled bikes down inside.