I've never done it before, but I know some women here have. They make big hard cases (and soft ones, too) to transport your bike in. You can take them on the airlines, but they'll charge you (an arm and a leg from what I understand). I've heard of people buying one of those gigantic suitcases, then taking the bike apart and putting it in there (removing both wheels, handlebars, pedals, etc). If you're going to be there a while, it might be worth the time it takes to break your bike apart to have it with you. I guess that would only work if your bike is a small frame tho.