I was in a touring pantomime a couple years back and the whole of our show fit into a 16-seater minibus, and was extremely portable. We had 7 flats, and they were all made in the same way.
The 'screen' itself was a 4 ft wide by 7 ft tall piece of thick material. It was thick in our case because it had to be painted as a backdrop - yours can be whatever material you like (however if you're getting changed behind it, in front if children, I recommend using material that is at least opaque). At the top and bottom of the material there was a 4.5 ft piece of wood attached with nails/staples/really strong glue - I think the flat itself was rolled around the wood once before being secured. The wood acted as a weight at the bottom of the screen, and as a means to keep the screen wide while on show. The top piece of wood had a short chain (about 4 inches long) attached to its centre.
To stand the screen up, all that was used was a large tripod stand - think ‘speaker stand’ and you're with me. We simply used a butcher's hook to attach the chain to the top of the tripod when it was extended at the right height.
The tripod folds flat, and the screen itself will roll very easily into a super-portable 4ft long piece of kit.
Tripods/
speaker standscome in at £30, but that’s only a very quick, completely non-indepth Froogle search. The wood I’m sure you can pick up from someone’s shed (my mate Pete’s got quite a bit), and the material is your choice. The chain and hook I’m sure you can find at B&Q or somewhere similar.
I hope that helps in some way or another.