If you're limiting yourself to carry-on, or even allowing for a (small) checked bag, there are bicycle panniers you can easily mount on the bike and then either carry aboard the plane or check.
Heck, you could pack a bicycle travel bag and pack your bike itself as checked luggage.
NYTimes Wirecutter has had some decent pannier reviews. I've had good luck with Arkel bags. Ortlieb look pretty bombproof.