Unfortunately, Deborah909 isn't totally correct.
A bacon cheeseburger would actually only be breaking one rule of Kashrut - eating meat which isn't Kosher (albeit twice). Eating beef which hasn't been killed according to the laws of Shechitah is no better or worse than eating pork (ie from an animal which can't be Kosher in the first place).
Furthermore, from the point of view of Halachah (Jewish law), meat which isn't Kosher isn't technically meat. Therefore, you wouldn't be breaking the law of eating milk and meat together, because the meat isn't technically meat. (As a side note, the law on meat and milk is stricter than that on not Kosher meat. It is allowed to own meat which isn't Kosher, and to "derive benefit" from it (eg you can purchase it and feed it to your pets, as long as it doesn't come into contact with your Kosher utensils). However, it's not permitted to even own or derive benefit from a milk-and-meat mixture.)
Cooking it on Shabbat, or eating it in a bread roll on Pesach, though, would be another issue.