I think you grossly underestimate the influence the United States Government holds over the Bahamas. Do you know what percentage of the Bahamas' economy is directly dependent on the United States? 95%? 98%? If the US asked the Bahamas not to sign a Chinese company, do you really think they'd say no?
Is there a American Company to buy Hutchinson's terminal lease Or do they want to sell?
And if they DID say no, what would we do, forbid our citizens the right to go to their country? Slap an embargo on them, like we did with Cuba?
Your idea would work great if we were a DICTATORSHIP.