I use a couple of Wescott Illuminator backdrops for video depositions and interview style shots. The backdrops are double sided; have an internal spring frame; and fold (or flip) up into a fairly small package. They're sized around 5'x7' when open.
If I remember correctly, I got 'em through B&H for around $140 apiece.
I have been looking for someone who sews to make me some for my cheap popup reflectors. Seems like it would not be hard to make another "bag" with four backgrounds instead of four reflector surfaces, especially with the original bag to use as a size/shape reference.