The United Kingdom does not have a double taxation agreement with Bahamas.
The United Kingdom does, however, have a tax information exchange agreement (TIEA) with Bahamas, which entered into force on 7 January 2011.
Details as to what information can be exchanged can be found in the agreement itself. If using the HMRC Intranet, the agreement can be viewed through the “New treaties/protocols in force” link on the sidebar, following the TIEAs link on the subsequent sidebar. On the HMRC web-site, searching for “TIEA Bahamas” will provide a link to the agreement.