I have an idea for a somewhat sturdy and cheap Strida bag...

Go to your local store that carries those folding deck chairs that people use for tailgating and outdoor concerts. These can usually be had for $10 to $20 (more if you're looking for a deluxe model). If you can, try to find a particularly tall one. The cool things about these is they come inside a canvas bag with a drawstring.

Now you have a dual purpose bag... Going to an the Pitchfork Festival? No problem... put the chair in the bag. Going to work... no problem, put the bike in the bag.

Sadly, you can't do the same with a 20" folder. Alternatively, you could look for a canvas laundry bag with a draw string for the same effect without the chair.

--sam