They will, apparently, still allow private charter flights. (Bahamas). But all commercial flights from US suspended immediately except to pick up departing passengers from the Bahamas back to the US.
St. Vincent & Grenadines PM also announced today that July 25th may be the last AA flight allowed in from Miami. He basically said the only reason he was allowing the incoming flight on the 25th was so Americans who flew in on the 18th had a way off the island. He 'strongly encouraged' all Americans to depart July 25th or risk being stranded.
From various travel blogs & forums, other Caribbean nations discussing following suit. Not good news for the US for Caribbean travel.