You can put it in a suitcase or carry on. Reduce the root ball and clip the oldest leaves if they are oversized. Put the plant in a baggie with the rootball wrapped in damp newspaper or paper towels to keep dust to a minimum.

You can also take the cut leaves in a plastic bag if you wish to start more.

Convention attendees bring back dozens of begonias in suitcases both in carry on and in checked bags without too many problems (some spilled soil, some broken leaves, maybe a decapitated stem but these can always be used to start more).

Too late to help with your question but if you're interested in begonias, be sure to look up the Potomac branch of the American Begonia Society!

Here is a link that might be useful: American Begonia Society