Yeah, a cheap duffel would work.
We've also used a woven type of bag which is popular here in Australia and also found in Japan. I haven't seen it elsewhere, but then I haven't looked. It can be found in shops in the airport and costs about $15. It doesn't have a long lifespan, but should work for a couple flights at least. The one I got worked for 4 flights.
In the photo below, there are:
-- a bicycle box each (Rowan's and mine)
-- a blue woven bag each containing the contents of our panniers ... the panniers themselves are in the bicycle boxes
-- a small duffel bag each, which folds up to almost nothing (Rowan's is green, mine is blue) as one piece of carry on ... we put our clothing in there
-- and a small carry on each ... Rowan used his handlebar bag, I used a small purple backpack which folded up to almost nothing.
And this is another shot of the woven bag ... it's handle came apart right at the end of the trip. But it survived a flight from Japan to London, London to Vancouver, Vancouver to Perth, Perth to Melbourne, and a rather chaotic journey of trains, busses and walking from Melbourne to our destination town a bit north of Melbourne.