Not sure where you are thinking about purchasing a double burger...but according to Allears, at both Pecos Bills and Cosmic Rays in the MK the double burgers (with bacon) and fries are $7.29. If you add $.85 for the cost of the extra bun, it's $8.14. Divide by 2 people, and it's $4.07, not including tax. A single burger with bacon (for comparison) is $5.29 plus $.79 for the bacon, total $6.08. Saves roughly $2 per person assuming each would purchase the singles otherwise...
Just FYI, I did some further calculating and found the savings are less (only a little over $1) if you are splitting with a child who would otherwise have a kids' meal for $3.99.