I admit I'm not speaking from actual experience, but I've had friends take apart their bikes and box them in the kind of cardboard boxes that bikes come in when originally shipped to a bike shop (can be purchased from most bike shops or picked up from their recycling bin behind the building). and then pack their clothes around the bike instead of using packaging foam and cardboard, although I guess you have to be careful about getting grease on your clothes. Then they use that as their check in luggage (without any extra charge or so I've heard) and then their standard carry on. There is a bike shop in Saratoga that rents bike boxes for about $30 a week (but it's not advertised, you would have to ask about it specifically), i wish i could remember the name of the shop, but i don't know if that would help in this situation. If you work for a business that has a location near where you're going, you can try doing a store to store shipment, which can be free or very inexpensive, but I'm not sure how many companies are willing to do that.