Prior to the latest lockdown, the USVI was requiring evidence of a negative test only if you were arriving from one of the "high impact" areas. Right now, I would expect the BVI is not considered a "high impact" area but that could change if their recently detected cases turn into a major outbreak. The USVI was also screening with a questionnaire and they had announced they were doing temperature checks on arriving passengers.

I haven't seen any evidence of coordination between the USVI and BVI. It would be nice to see some coordination of policies and procedures throughout the Caribbean - it would certainly make things easier for people who want to island hop or are connecting through to their destination.

Here's a snippet from: https://usviupdate.com/2020/07/u-s-virgin-islands-launches-online-portal-to-prescreen-all-travelers/

"Upon visiting the portal, all travelers will be greeted with a welcome that guides them through a series of screens, including General Information, Terms and Conditions, Traveler Information, and the COVID-19 Traveler Screening Tool. After travelers from highly impacted areas upload their COVID-19 test results, the information submitted will be processed in 24-48 hours and a certification code issued immediately upon completion.

For most travelers, the portal screening and certification will eventually replace the existing manual procedure, which requires the physical completion and review of the COVID-19 Traveler Screening Tool at the Territory’s ports of entry. Once the passenger arrives, the Virgin Islands Port Authority, in conjunction with the Department of Health and the Virgin Islands National Guard, will process the traveler using the validation generated from the portal in addition to performing temperature checks with a thermal scanner."