Flying with a folding bike can be expensive. Most Dahon models will fit into the company's semi-hard Airporter case (even if it is a really tight squeeze for the 24" and 26" models). But it is an pricey piece of luggage costing upwards of $300.
Even its Airporter Mini, for its 16" and 20" bikes, is pushing that price point. Brompton's Travel Suitcase is more expensive still. You might consider it worth it as it is compact enough that you might be allowed it as a carry-on.
The other cost to flying with a folding bike is that the airlines lose no opportunity to impose an overweight baggage surcharge that can easily top $100.
A new product from Taiwanese manufacturer, Tern, might let you dodge that by having your bike travel in mufti. It has launched a set of protective pads for its — or any other — 20" folding bike so you can pack it into any standard hardshell 31" suitcase. Its nine-piece $75 Tern FlightSuit kit (above) includes padded nylon custom protectors for a bike’s seatpost, handlepost, pedals and dropouts. Suitcase not included.
You'll need a bigger suitcase for larger bikes, or to buy from Tern's own range of semi-hard nylon Airporter cases. Those run from $300 upwards.
One tip: if an airline clerk asks at check-in what's in that large, heavy looking bag of yours, smile sweetly and go for an innocent sounding euphemism like "personal mobility device." You might get away with it.