|Fits neatly under your saddle...|
But if that 'thing' is bagged up - it's a piece of luggage and who's to say that you can't take luggage onboard.
Performing the role of the bag - Tern have developed the CarryOn Cover, which slips over your 20-inch folding bike and allows you to carry it around with a shoulder strap. Very neat and practical. Good news is that they are now available in South Africa too, so freedom from authorities awaits.
|...and over your shoulder|