In the case of a civil ceremony in Barbados, this is conducted through a basic British system of the Magistrates Court, which sanctions only a magistrate to conduct weddings (not a JP).
Your first step is to decide which Parish you would like to be married in, then proceed to approach the District Court there-in to obtain your letter of intent to marry to produce to the ministry. This may incur a fee. After applying for the license with the Ministry of Home Affairs, you will need to register the marriage with the original District Court where you stated your intent. This may also incur a fee of $100 Bds and an additional stamp duty of $25 Bds.
Please note that a marriage is considered legal in Barbados if it is performed before 9 p.m. (This is set by the Ministry Of Home Affairs). Some magistrates will not perform after 6 p.m. so it is important that you discuss everything with your ceremony magistrate.