Take it with you on the plane. I brought mine with me when I came here. Didn't charge me a penny. Mind you I only had one suitcase. If you have two suitcases you might get charged.
Just pack it out in a box, take the stem off the steerer and the front wheel. Back wheel isn't necessary but means you can use a slightly smaller box. Take the pedals off too. Then pad it out with polystyrene like crazy.
Letting air out of the tires isn't necessary too, that rule is more for high pressure road tires, the difference in air pressures big fat trials tires won't make a difference.