Getting into these groups ain't easy. You must be an active and good poster around the Off-Topic forums where most of the members that take part in those various groups are active. Do NOT ask to be accepted because that will only shorten your chances of actually getting in. As I said, you have to be a quality poster and to make yourself known. If you do this, you'll eventually be picked up by any of these groups. When that happens, you'll be sent a Personal Message by either the leader of the group or by a certain member. These groups are like gangs, you chat in a separate hidden forum about random stuff. It usually takes about 1-2 years to get in, but if you make yourself really well known you can get in after a few months. Do NOT confuse these groups with those you see in the Gangs forum, we don't really do Multiplayer stuff.
These are the groups I'm talking of: $outh $ide Hoodz, Andolini Mafia Family, Leone Family Mafia, City Link, The Connection, The Precinct & Zaibatsu. You can find here
a much more detailed information related to Groups.
The "BUSTED!" group you've asked above about is only for banned members, so I don't believe you really wish to get in it.