They have charter flights that are allowed for only certain people... these include:
Former exiled Cuban Citizens visiting family, news reporters, aide workers, government officials, and people on official company business (such as a head of CO
visiting the airline officials there).
Normally, people who are not on this list and want to go to Cuba from the US use a third party nation. They simply buy a ticket to Nassau, then in Nassau buy a Bahamasair ticket to Havana... same when coming back. You can't buy tickets to Cuba from the US, even if you're connecting, you must buy the ticket in the interveening nation. Other options are Mexico, Canada, or Jamaica.
I know that's how Cubans here send money and presents to family in cuba, the courier companies send them through mexico or the bahamas.
Charters are allowed, but they must be approved. The government approved ones we have now are for the people on the above list.