All travelers need a BVI Gateway Traveller Authorisation Certificate which can be obtained via an online portal, called BVI Gateway at http://bvigateway.bviaa.com/. Applications must begin no later than 48 hours prior to traveling and must be complete at least 24 hours before travel date and time.
Children under the age of 2 are exempt from presenting a COVID-19 test.
Travelers with proof of recovery from the virus within the last 90 days prior to boarding. Proof of a recent positive viral test and a letter from your healthcare provider or a public health official stating that you were cleared to travel.
More info at the CDC site
Travelers who did not get tested, are advised to stay home and self-quarantine for 10 days after travel.