Bloomie has a special treaty with Bermuda for his island. The government of Bermuda exercises no authority there, so Bloomberg has his own private military.
I assume they're armed with more than high-cap handguns and automatic weapons. He's hinted at his anti-aircraft and anti-ship capabilities. And he buys them all on the worldwide arms free market, rather than having snitches try a strawman purchase on some FFL-licensed gun dealer in Podunk, Wyoming.