For clarification, the bags are plastic, not the citrus fruit, in case there was any confusion.
This was super easy to make and only took a minute or two. I simply wadged up one bag and stuffed it into the bottom of the second one, then twisted the outer bag and turned it inside out, twisted, repeat, until there was no more bag. Then I threaded a piece of string around the bag opening, pulled it tight, knotted it and vwahlah! Scrubby Buddy! Works just like the $2.50 one at the store. Only it cost $2.50 less, is keeping the plastic out of the landfill, and Scrubbybuddy Corp. will produce one fewer of their flagship plastic products (at what I now know is a 2500% markup).
If that doesn't work, I'll report it and my next solution in an update to this post. We're getting into citrus season so I'm sure I'll come across plenty of bags to experiment with while creating the perfect upcycled dish scrubby buddy.
UPDATE: 5.24.13 ~ The solution was a smashing success. The scrubby buddy held together for seven months before getting a tear (from cleaning a knife). To fix it, I stuffed it all back in through the tear and put it into a new citrus bag. Twist, invert, repeat and tie off as detailed. Works like a champeeen!