I was in the V.I for almost 10 years. They have the safari system set up but it only runs on the tourist routes. So you're out of luck unless you lived on one of the two main routes that had the safaris.
When the ports were full of cruise ships, you could expect to spend 45+ minutes getting from Charlotte Amalie to Red Hook. Sometimes I spent an hour going from Charlotte Amalie to Havensight. That was only a distance of about 2 miles.
The V.I is extremely corrupt and the taxi unions there have a great deal of influence. That's why the public transportation never improved while I lived there.
Not Just Bikes did a great rant on the carbrain of The Bahamas: https://www.youtube.com/watch?v=kdz6FeQLuHQ