http://www.bahamas-travel.org/bahamas-cruise-travel/
Can a permanent U.S. resident travel on a cruise to the Bahamas?
And if so, what documents are needed? Green card or home-country passport, or both?
Lawful Permanent Residents (Green card holder’s) do NOT need a passport to enter the United States, however you may need a passport to enter another country. Please contact the embassy of the foreign country you will be traveling to for their requirements.
https://help.cbp.gov/cgi-bin/customs.cfg/php/enduser/std_adp.php?p_faqid=74&p_created=1043364936&p_sid=*2_saiBj&p_accessibility=0&p_redirect=&p_lva=1026&p_sp=cF9zcmNoPTEmcF9zb3J0X2J5PSZwX2dyaWRzb3J0PSZwX3Jvd19jbnQ9MjcwLDI3MCZwX3Byb2RzPTAmcF9jYXRzPTAmcF9wdj0mcF9jdj0mcF9wYWdlPTEmcF9zZWFyY2hfdGV4dD0iUGVybWFuZW50IFJlc2lkZW50Ig**&p_li=&p_topview=1 ..
Permanent Residents of the United States do not require a visa to travel to The Bahamas. However, Permanent Residents of the United States are required to have an Alien Registration Card (Green Card) with a valid passport from the country of origin.
http://www.un.int/bahamas/tourist%20visa%20info.htm ..
Bahamas Cruise