I guess "bacon" acts like an adjective here, or, more correctly, it's probably an attributive. So which order is correct? I tried googling; "two bacon double cheeseburgers" yielded more results (28 800 000 vs 9 060 000). Nevertheless, I am so curious I wish to know which grammar rule applies here. One minor problem is that electronic translators (machines) sometimes treat the word "double" in "two bacon double cheeseburgers" as a verb. It's obviously wrong, of course.
This is simply the name used by a popular fast food franchise.
There are two burgers, each with cheese (hence "double cheeseburger") and bacon as an extra. You might say "double cheeseburger with bacon" But the name of the product is "Bacon Double Cheeseburger". There isn't a rule being applied in a consistent way.