I visited Barbados in August 2014 as a member of a wedding party. We did not stay in Bridgetown, but I visited it twice during the week. The first time, two friends and I caught a lively bus to the colourful town centre where we ate a lunch of jerk fish, cow heel soup and fried chicken in an orange sauce.
A few days later we bussed again down the island's main highway to the sound of bashment music. We walked along the beach from the city centre and through the Barbados Yacht Club to see the garrison (taking care to avoid stepping on any evil Stonefish). On arrival we found a square of colonial-era buildings around a racecourse, which was rather underwhelming. The Barbados Museum cost B$12 to enter, and gives a decent overview of the island's history. Of particular interest to me were the theories as to what caused the extinction of the indigenous Amerindians, who has completely disappeared by the time the Brits arrived.