In the comics, Wolverine has a long, cloudy history. For many years (from his creation in the mid-1970s until the "House of M" storyline circa 2005, I believe) Wolverine himself didn't remember much of his history; memories prior to the adamantium being applied to his bones were almost completely absent, or impossibly confused and tangled. Given his long life, we've only gotten glimpses of his history even now: by analogy, a photo album rather than a video of his entire life. And, even then, a photo album with most of the pages missing.
We do know that Wolverine worked for the government for a significant period of time. That could well include the 1960's, when the X-Men: Days of Future Past movie was set. It's entirely possible that he could have been acting as an undercover agent and working for the Mafia at that time.
That said, I am unaware of any Wolverine story in the comics explicitly establishing that he worked as a bodyguard for a notable period of time, or working for the Mafia for a notable period of time.